Curriculum Vitæ
Ricardo Martins da Silva ROSA
Professor Adjunto I
Depto. de Matemática Aplicada - Instituto de Matemática
Universidade Federal do Rio de Janeiro
Caixa Postal 68530 Ilha do Fundão
Rio de Janeiro RJ 21945-970 BRAZIL
April 6, 2007
Education
• Doctorate Degree
1992 to 1996 - PhD in Applied Mathematics, Indiana University, USA. Graduation date: December 30, 1996. Thesis advisor: Roger Temam. Title of the thesis: “Attractors for Weakly
Dissipative Equations. Inertial Manifolds and Normal Hyperbolicity. Approximate Inertial
Manifolds of Exponential Order.”
• Master of Science Degree
1989 to 1992 - Master of Science in Mathematics, Universidade Federal do Rio de Janeiro,
Brazil. Graduation date: August 5, 1992. Thesis advisor: Felipe Acker. Title of the thesis:
’‘Uma Análise Qualitativa do Processo de Discretização via Diferenças Finitas de Equações de
Reação e Difusão.”
• Bachelor Degree
1986 to 1989 - Bachelor in Mathematics, Universidade Federal do Rio de Janeiro, Brazil.
Graduation date: September 25, 1991.
Professional Experience
• Since August 1993 - Professor of Mathematics, full-time, Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brazil.
• February and March, 1999 - Visiting Professor at Université de Paris-Sud, Orsay, France
• October, 2004 - Visiting Professor at Université de Picardie - Jules Verne, Amiens, France
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Research Activities
• Articles published in scientific journals
1. Asymptotic regularity conditions for the strong convergence towards weak limit sets and
weak attractors of the 3D Navier-Stokes equations, Journal of Differential Equations 229
(2006), no. 1, 257-269.
2. (with C. Foias, M. Jolly, O. Manley, and R. Temam) Kolmogorov theory via finite-time
averages, Physica D, 212 (2005), no. 3-4, 245–270.
3. (with M. Jolly) Computation of non-smooth local center manifolds, IMA Journal of Numerical Analysis, 25 (2005), no. 4, 698–725.
4. (with M. Cabral), Chaos on a damped and forced KdV equation, Physica D, 192 (2004),
no. 3 & 4, 265–278.
5. (with M. Cabral and R. Temam), Existence and dimension of the attractor for the Bénard
problem on channel-like domains, Discrete and Continuous Dynamical Systems A, 10
(2004), no. 1& 2, 89–116.
6. (with I. Moise and X. Wang) Existence of uniform attractors for noncompact nonautonomous dissipative systems via energy equations, Discrete and Continuous Dynamical
Systems A, Discrete and Continuous Dynamical Systems A, 10 (2004), no. 1& 2, 473–496.
7. Exact finite-dimensional feedback control via inertial manifold theory with application to
the Chafee-Infante equation, J. Dynamics and Diff. Eqs. 15 (2003), no. 1, 61–86.
8. (with C. Foias, M. S. Jolly and O. P. Manley), On the Landau-Lifschitz degrees of freedom
in 2-D turbulence, J. Stat. Phys. 111 (2003), no. 3/4, 1017–1019.
9. (with O. Goubet) Asymptotic smoothing and the global attractor of a weakly damped
KdV equation on the real line, J. Diff. Eqs., 185 (2002), 25–53.
10. Some results on the Navier-Stokes equations in connection with the statistical theory of
stationary turbulence, Applications of Mathematics, 47 (2002), no. 6, 485–516.
11. (with C. Foias, M. Jolly, and O. P. Manley) Statistical estimates for the Navier-Stokes
equations and the Kraichan theory of 2-D fully developed turbulence, J. Stat. Phys. 108
(2002), no. 3/4, 591–646.
12. (with C. Foias, O. P. Manley, and R. Temam) Estimates for the energy cascade in threedimensional turbulent flows, Comptes Rendus Acad. Sci. Paris, Série I, 333 (2001), no.
5, 499–504.
13. (with M. Jolly and R. Temam) Accurate computations on inertial manifolds, SIAM J.
Sci. Computing 21 (2001), no. 6, 2216–2238.
14. (with C. Foias, O. P. Manley and R. Temam) Cascade of energy in turbulent flows,
Comptes Rendus Acad. Sci. Paris, Série I, 332 (2001), no. 6, 509–514.
15. The global attractor of a weakly damped, forced Korteweg-de Vries equation in H 1 (IR),
Matemática Contemporânea 19 (2000), 129–152.
16. (with M. Jolly and R. Temam) Evaluating the dimension of an inertial manifold for the
Kuramoto-Sivashinsky equation, Advances in Differential Equations 5 (2000), no. 1-3,
31-66.
17. (with I. Moise and X. Wang) Attractors for non-compact semigroups via energy equations,
Nonlinearity 11 (1998), no. 5, 1369-1393.
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18. The global attractor for the 2D Navier-Stokes flow on some unbounded domains, Nonlinear Analysis TMA, 32 (1998), no. 1, 71-85.
19. (with I. Moise) On the regularity of the global attractor for a weakly damped, forced
Korteweg-de Vries equation, Advances in Differential Equations, 2 (1997), no. 2, 267296.
20. (with R. Temam) Inertial manifolds and normal hyperbolicity, ACTA Applicandae Mathematicae, 45 (1996), 1-50
21. (with N. Castañeda) Optimal estimates for the uncoupling of differential equations, J.
Dynamics and Diff. Eqs. 8 (1996), no. 1, 103-139.
22. Approximate inertial manifolds of exponential order, Discrete and Continuous Dynamical
Systems 1 (1995), no. 3, 421-448.
23. Conjugacy of strongly continuous semigroups generated by normal operators, J. Dynamics
and Diff. Eqs., 7 (1995), no. 3, 471-490.
• Complete articles published in annals of congresses
24. (with R. Temam) Finite-dimensional feedback control of a scalar reaction-diffusion equation via inertial manifold theory, in Foundations of Computational Mathematics, Selected
papers of a Conference held at IMPA, Rio de Janeiro, RJ, Brazil, January 1997 (Eds. F.
Cucker and M. Shub), pp. 382-391, Springer-Verlag, Berlin, 1997.
• Articles submitted for publication
25. (com L. Dieci, M. Jolly e E. Van Vleck) Error in approximation of Lyapunov exponents
on Inertial Manifolds: the Kuramoto-Sivashinsky equation.
• Books published
1. (with C. Foias, O. P. Manley, and R. Temam) Navier-Stokes Equations and Turbulence,
Encyclopedia of Mathematics and its Applications 83, Cambridge University Press, Cambridge, 2001.
• Book chapters
1. Turbulence Theories, In: J.-P. Franoise; G.L. Naber; Tsou S.T.. (Org.). Encyclopedia of
Mathematical Physics, Elsevier, Oxford, Vol. 5 pp. 295-302, 2006.
• Summaries published in Annals of Congresses
1. On the existence and regularity of the global attractor of the 2D Navier-Stokes equations,
510 SBA, Florianópolis, SC, Brazil, May 24-27, 2000
2. The global attractor for a weakly damped, forced Korteweg-de Vries equatin on the real
line, 49o SBA, IMECC-Unicamp, Campinas, SP, May 26-29, 1999.
3. The global attractor of the 2D Navier-Stokes equations on channel-like domains, XX
CNMAC, Gramado, RS, Brazil, September 1997.
4. (with R. Temam) Inertial manifolds and normal hyperbolicity, AMS Regional Meeting,
Orlando, Florida, March 17 and 18, 1994.
• Participation in Conferences
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– V Escola de Primavera em Transio e Turbulncia, IME, Rio de Janeiro, RJ, September
25 to 29, 2006. Talk: “Equaes de Navier-Stokes e turbulncia”, September 25, 2006.
– II Escola Brasileira de Equaes Diferenciais (EBED), IMPA, Rio de Janeiro, RJ, Janurary
23 to 27, 2006. Talk: “Asymptotic results related to the 3D incompressible Navier-Stokes
equations”, Januray 25, 2006.
– Workshop on Partial Differential Equations 60th Birthday of Prof. Gustavo Perla Menzala, Petrpolis, RJ, August 10 to 12, 2005. Talk: “Regularity issues related to the
asymptotic behavior of solutions of the Navier-Stokes equations”, August 10. 2005.
– ENCIT 2004 - 10th Brazilian Congress of Thermal Engineering and Sciences, Glória
Hotel, Rio de Janeiro, Brazil, November 29 to December 3, 2004. Talk: “Theoretical
aspects of homogeneous isotropic turbulence,” November 30, 2004.
– I Escola Brasileira de Equações Diferenciais (EBED), IMECC-Unicamp, Campinas, SP,
Brazil. Short-course: “Resultados recentes sobre as equações de Navier-Stokes para fluidos incompressı́veis,” June 9-13, 2003.
– SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, USA, May 2631, 2003. Talk: “Estimates for the Navier-Stokes equations pertaining to the statistical
theory of 3D stationary turbulence,” May 29, 2003.
– Programa de Verão do LNCC, Petrópolis, RJ, Brazil. Short-course: “Equações de NavierStokes e turbulência,” February 24-27, 2003.
– Second International Conference on Semigroup of Operators, Theory and Applications
(SOTA 2), Rio de Janeiro, Brazil, September 10-14, 2001. Talk: “Asymptotic smoothing
and the global attractor of a weakly damped KdV equation on the real line”
– Seventh Paseky School on Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic Tcheca, June 3-10, 2001. Five lectures on “Navier-Stokes equations and the statistical theory of turbulence”
– Jornadas de Matemática Aplicada e Computacional - Tópicos em Turbulência, LNCC,
RJ, Brazil, May 7-8, 2001. Talk: “Soluções estatı́sticas das equações de Navier-Stokes e
aplicações na teoria convencional de turbulência”
– September 15-17, 2000 - Conference on Nonlinear Problems in Applied Sciences, Bloomington, IN, USA
– May, 24-27, 2000 - 51o Seminário Brasileiro de Análise, Florianópolis, SC, Brazil. Talk:
“On the existence and regularity of the global attractor of the 2D Navier-Stokes equations”
– March 7-8, 2000, Conférence en l’honneur de Roger Temam, Université de Paris-Sud,
Orsay, France
– October 23-24, 1999, Fall 1999 Midwest Partial Differential Equations Seminar, University
of Illinois, Urbana-Champaign, IL, USA
– October 8-10, 1999, AMS Regional Meeting, University of Texas, Austin, USA
– July 19-23, 1999 - IV Workshop on Partial Differential Equations, IMPA, Rio de Janeiro,
RJ, Brazil. Talk: “Existence and regularity of global attractors for a weakly damped,
forced KdV equation.”
– May 26-29, 1999 - 49o Seminário Brasileiro de Análise, IMECC-Unicamp, Campinas,
SP, Brazil. Talk: “The global attractor of a weakly damped, forced Korteweg-de Vries
equation on the real line;” joint work with I. Moise and X. Wang.
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– January 5-12, 1997 - The Foundations of Computational Mathematics (FoCM), IMPA, Rio
de Janeiro, RJ, Brazil. Talk: “Finite-dimensional feedback control of a scalar reactiondiffusion equation via inertial manifold theory;” joint work with R. Temam.
– June 1-5, 1996 - CBMS-NSF Regional Conference on Approximation Dynamics, University of Missouri-Columbia, USA.
– March 17-18, 1994 - AMS Regional Meeting, Orlando, Florida, USA. Talk: “Inertial
manifolds and normal hyperbolicity;” joint work with R. Temam.
• Scientific Visits
– Deceber 3 to 6, 2006, University of Texas A& M, USA.
– November 15 to December 11, 2006, Indiana University, USA
– August 21 to Semptember 20, 2006, Indiana University, USA
– August 22 to September 10, 2005, Indiana University, USA
– October 2004, Université de Picardie - Jules Verne, Amiens, France.
– September and November, 2004, Indiana University, USA
– May 20 to 26, 2003, University of Southern California, CA, USA
– May 13 to 19, 2003, Indiana University, IN, USA
– March 18 to May 17, 2002, Université de Paris-Sud, Orsay, France
– March 18 to May 17, 2002 - Université de Paris-Sud, Orsay, France.
– February 28 to March 7, 2001 - Texas A&M, TX, EUA
– Januray 12 to March 11, 2001 - Indiana University, IN, EUA
– August 30 to September 30, 2000 - Indiana University, IN, EUA
– September 1, 1999 to April 29, 2000 - Indiana University, IN, EUA
– February 28 to March 30, 2000 - Université de Paris-Sud, Orsay, France
– February 14 to March 13, 1999 - Université de Paris-Sud, Orsay, France.
– August 23-28, 1998 - Indiana University, IN, EUA.
– August 10-22, 1998 - CNLS, Los Alamos National Lab, NM, EUA.
– February 2 to March 3, 1998 - Université de Paris-Sud, Orsay, France.
– May 4 to June 3, 1996 - Université de Paris-Sud, Orsay, France.
• Other Talks
– November 15, 2004, “Statistical estimates for the Navier-Stokes equations in relation to
turbulence,” PDE Seminar, Indiana University, IN, USA
– October 17, 2004, “Statistical estimates for the Navier-Stokes equations in relation to
turbulence,” Université Jules Verne, Amiens, France.
– May 23, 2003, “Asymptotic regularity for a weakly damped and forced Korteweg-deVries
equation,” University of Southern California, CA, USA
– May 23, 2003, “Estimates for the Navier-Stokes equations pertaining to the statistical
theory of 3D stationary turbulence,” University of Southern California, CA, USA
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– March 25, 2002, “Navier-Stokes equations and the statistical theory of turbulence”, Université Jules Verne, Amiens, France.
– March 5, 2001, “Statistical results for the 2D Navier-Stokes equations”, Partial Differential Equations in Fluid Dynamics Seminar, Texas A&M, TX, EUA
– September 25, 2000, “Asymptotic smoothing and the global attractor of a weakly damped
KdV equation on the real line”, PDE Seminar, Indiana University, IN, EUA
– April 3, 2000, “Regularity of the attractor for the 2D Navier-Stokes equations on nonsmooth domains”, PDE Seminar, Indiana University, IN, EUA
– February 23, 2000, “Regularity of solutions of the 2D Navier-Stokes equations on nonsmooth domains”, Differential Equations Seminar, Indiana University, IN, EUA
– November 5, 1998, “Tópicos na teoria de sistemas dinâmicos em dimensão infinita”,
Seminário de Equações Diferenciais, IMECC-UNICAMP, Campinas, SP.
– August 26, 1998, “The global attractor for non-compact semigroups via energy equations”, ISC-Seminar, Indiana University, IN, EUA.
– August 17, 1998, “The role of energy equations in the existence proof of global attractors
for non-compact semigroups”, Navier-Stokes Equations and Turbulence Seminar, CNLS,
Los Alamos National Lab, NM, EUA.
– October 14, 1997, “Sistemas dinâmicos em dimensão infinita”, Seminário de Equações
Diferenciais Parciais, IMPA, RJ.
Professional Activities at the Graduate Level
• Lectures
– June 25 to July 11, 1996 - Short-course in Dynamical Systems in Infinite Dimensions,
Departamento de Matemática Aplicada, IM-UFRJ, Brazil.
– Second semester 1997 - Dynamical Systems - Graduate program in Applied Mathematics,
IM-UFRJ, Brazil.
– First semester 1998 - Functional Analysis - Graduate program in Applied Mathematics,
IM-UFRJ, Brazil.
– Second semester 2000 - Sobolev Spaces and Eliptic Equations - Graduate program in
Applied Mathematics, IM-UFRJ, Brazil.
– Second semester 2000 - Dynamical Systems - Graduate program in Applied Mathematics,
IM-UFRJ, Brazil.
– Second semester 2000 - Linear and Nonlinear Semigroups - Graduate program in Applied
Mathematics, IM-UFRJ, Brazil.
– First semester 2002 - Dynamical Systems - Graduate program in Applied Mathematics,
IM-UFRJ, Brazil.
– First semester 2003 - Functional Analysis - Graduate program in Applied Mathematics,
IM-UFRJ, Brazil.
– First semester 2004 - Dynamical Systems - Graduate program in Applied Mathematics,
IM-UFRJ, Brazil.
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– First semester 2005 - Dynamical Systems - Graduate program in Applied Mathematics,
IM-UFRJ, Brazil.
– First semester 2006 - Partial Differential Equations - Graduate program in Applied Mathematics, IM-UFRJ, Brazil.
• Master of Science students
– May 31, 2006, Adriano Maurcio de Almeida Crtes, “Conjuntos de Aubry-Mather no
contexto dos mapeamentos twist,” Master of Science degree in Applied Mathematics,
IM-UFRJ.
– July 31, 2006, Raphael Carlos Santos Machado, “Criptossistemas dinmicos,” Master of
Science degree in Applied Mathematics, IM-UFRJ.
– August 22, 2003, Fábio Ramos, “Métodos geométricos em transporte lagrangiano,” Master of Science degree in Applied Mathematics, IM-UFRJ.
– December 27, 2002, Luciana Santos Silva, “Solução numérica para um escoamento geofı́sico aplicado ao rio Amazonas,” Master of Science degree in Applied Mathematics,
IM-UFRJ.
– May 27, 2002, Sérgio Krakowski, “Estudo de caos em um sistema dinâmico em dimensão
infinita,” Master of Science degree in Applied Mathematics, IM-UFRJ.
– March 30, 2001, Patrı́cia Sañez, “Atrator Global para as Equações de Navier-Stokes em
Domı́nios Irregulares,” Master of Science degree in Applied Mathematics, IM-UFRJ
Professional Activities at the Undergraduate Level
• Lectures
– First semester 1997 - Cálculo Infinitesimal III - Computer Science, UFRJ (Mutivariable
Integral Calculus).
– Second semester 1997 - Cálculo Infinitesimal II - Computer Science, UFRJ (Mutivariable
Differential Calculus).
– First semester 1998 - Cálculo Infinitesimal I - Computer Science, UFRJ (First-Year Differential and Integral Calculus).
– Second semester 1998 - Projetos de Matemática Aplicada A - Mathematics, UFRJ (Projects
in Applied Mathematics).
– First semester 1999 - Algebra Linear II - Engineering, UFRJ (Linear Algebra).
– First semester 1999 - Cálculo Vetorial e Geometria Analı́tica - Computer Science, UFRJ
(Vector Calculus and Analytic Geometry).
– Second semester 2001 - Algebra Linear II - Engineering, UFRJ (Linear Algebra).
– First semester 2002 - Algebra Linear II - Engineering, UFRJ (Linear Algebra).
– Second semester 2002 - Equações Diferenciais - Mathematics, UFRJ (Differential Equations).
– First semester 2003 - Equações Diferenciais - Mathematics, UFRJ (Differential Equations).
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– Second semester 2003 - Equações Diferenciais - Mathematics, UFRJ (Differential Equations).
– Second semester 2003 - Algebra Linear II - Engineering, UFRJ (Linear Algebra).
– First semester 2004 - Equações Diferenciais - Mathematics, UFRJ (Differential Equations).
– First semester 2005 - Equações Diferenciais - Mathematics, UFRJ (Differential Equations).
– Second semester 2005 - Equações Diferenciais - Mathematics, UFRJ (Differential Equations).
– First semester 2006 - Equações Diferenciais - Mathematics, UFRJ (Differential Equations).
– First semester 2007 - Modelagem Matemática - Mathematics, UFRJ (Math. Modeling).
Prizes and Grants
• Prizes
– Prêmio Antônio Luı́s Vianna 1998-2000 for recent graduates - UFRJ/FUJB, November
2000 (R$ 15.000,00 financial support).
– John Ewing Book Award 1996 - Indiana University (US$300 in Springer-Verlag books).
• Grants
– Mar/2007 to Fev/2010 - Research fellowship from CNPq, Brası́lia, Brazil.
– Aug/2003 to Fev/2007 - Research fellowship from CNPq, Brası́lia, Brazil.
– Aug/2001 to Jul/2003 - Research fellowship from CNPq, Brası́lia, Brazil.
– Aug/1999 to Jul/2001 - Research fellowship from CNPq, Brası́lia, Brazil.
– Program ”Antônio Luı́s Vianna”. Financial support of R$5,000.00 for recent graduates.
UFRJ-FUJB.
– Aug/1997 to Jul/1999 - Research fellowship from CNPq, Brası́lia, Brazil.
– Sep/1992 to Dec/1996 - Scholarship from CNPq for graduate studies at the Indiana
University, USA.
– Sep/1989 to Feb/1992 - Scholarship from CNPq for Master of Science studies at UFRJ,
Brazil.
– Mar/1988 to Feb/1989 - Undergraduate fellowship from CNPq at UFRJ, Brazil.
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