Equação de Burgers em um Domínio Arbitrário

Authors

  • L.A. FIOREZE
  • J.P. LUKASZCZYK

DOI:

https://doi.org/10.5540/tema.2002.03.01.0101

Abstract

Neste trabalho provamos a existência e unicidade de soluções fracas para a equação vetorial de Burgers em domínios arbitrários em três dimensões. A única hipotese considerada sobre o domínio é que este seja um aberto. As estimativas para estes resultados utilizam uma desigualdade de Sobolev do tipo elíptica apresentada nos preliminares.

References

[1] R. Adams, Sobolev Spaces", Academic Press, New York, 1975.

H. Brezis, Analyse Fonctionnelle", 2a Tiragem, Masson S. A., 1987.

J.M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Math., 1 (1948), 171-199.

E.A. Coddington e N. Levinson, Theory of Ordinary Dierential Equations", McGraw Hill, 1955.

L.C. Evans, Partial Dierential Equations", Berkeley Mathematics Lectures Notes, V. 3A, Berkeley, Ca, 1993.

J.B. Heywood e W. Xie, Smoth solution of the vector Burgers equation in nonsmooth domains, Dierential and Integral Equations, 10, No. 5 (1997), 961-974.

J.B. Heywood, The Navier-Stokes equations: on the existence, regularity and decay of solutions, Indiana University Mathematics Journal, 29, No. 5 (1980), 639-681.

L.A. Medeiros e E.A. Milla, A Integral de Lebesgue { Texto Didático", Série Matemática / 1, Editora Universitária, 1989.

R. Temam, Navier-Stokes Equations - Theory and Numerical Analysis", North-Holland Publishing Company, Amsterdam-New York-Oxford, 1979.

W. Xie, A sharp pointlibie bound for functions with L2 laplacions and zero boundary values on arbitrary three-dimensional domains, Indiana University Mathematics Journal, 40 (1991), 1185-1192.

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Published

2002-06-01

How to Cite

FIOREZE, L., & LUKASZCZYK, J. (2002). Equação de Burgers em um Domínio Arbitrário. Trends in Computational and Applied Mathematics, 3(1), 101–110. https://doi.org/10.5540/tema.2002.03.01.0101

Issue

Vol. 3 No. 1 (2002)

Section

Original Article

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