Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Pseudo-advection method for the two-dimensional stationary Euler equations


Author: Takahiro Nishiyama
Journal: Proc. Amer. Math. Soc. 129 (2001), 429-432
MSC (2000): Primary 35Q30, 76B03
DOI: https://doi.org/10.1090/S0002-9939-00-05748-8
Published electronically: August 28, 2000
MathSciNet review: 1800232
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

The existence of generalized solutions to the two-dimensional stationary Euler equations with nonvanishing vorticity is proved by a new method completely different from the usual variational approaches.


References [Enhancements On Off] (What's this?)

  • 1. T. V. Badiani, Existence of steady symmetric vortex pairs on a planar domain with an obstacle, Math. Proc. Cambridge Philos. Soc. 123 (1998), 365-384. MR 98m:76029
  • 2. G. R. Burton, Steady symmetric vortex pairs and rearrangements, Proc. Roy. Soc. Edinburgh 108A (1988), 269-290. MR 89f:35178
  • 3. G. F. Carnevale and G. K. Vallis, Pseudo-advective relaxation to stable states of inviscid two-dimensional fluids, J. Fluid Mech. 213 (1990), 549-571. MR 91c:76058
  • 4. A. R. Elcrat and K. G. Miller, Rearrangements in steady vortex flows with circulation, Proc. Amer. Math. Soc. 111 (1991), 1051-1055. MR 91g:35205
  • 5. R. Temam, On the Euler equations of incompressible perfect fluids, J. Funct. Anal. 20 (1975), 32-43. MR 55:3573
  • 6. B. Turkington, On steady vortex flow in two dimensions. I, Comm. Partial Differential Equations 8 (1983), 999-1030. MR 85g:35110
  • 7. -, On steady vortex flow in two dimensions. II, Comm. Partial Differential Equations 8 (1983), 1031-1071. MR 85g:35110
  • 8. G. K. Vallis, G. F. Carnevale, and W. R. Young, Extremal energy properties and construction of stable solutions of the Euler equations, J. Fluid Mech. 207 (1989), 133-152. MR 90m:76026
  • 9. G. Wolansky, Existence, uniqueness, and stability of stationary barotropic flow with forcing and dissipation, Comm. Pure Appl. Math. 41 (1988), 19-46. MR 88k:35167

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35Q30, 76B03

Retrieve articles in all journals with MSC (2000): 35Q30, 76B03


Additional Information

Takahiro Nishiyama
Affiliation: Department of Mathematics, Keio University, Yokohama 223–8522, Japan
Email: nisiyama@math.keio.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-00-05748-8
Keywords: Two-dimensional stationary Euler equations, vorticity, Galerkin method, pseudo-advection
Received by editor(s): April 15, 1999
Published electronically: August 28, 2000
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society