Pseudo-advection method for the two-dimensional stationary Euler equations
HTML articles powered by AMS MathViewer
- by Takahiro Nishiyama PDF
- Proc. Amer. Math. Soc. 129 (2001), 429-432 Request permission
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
- T. V. Badiani, Existence of steady symmetric vortex pairs on a planar domain with an obstacle, Math. Proc. Cambridge Philos. Soc. 123 (1998), no. 2, 365–384. MR 1490208, DOI 10.1017/S0305004197002041
- G. R. Burton, Steady symmetric vortex pairs and rearrangements, Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), no. 3-4, 269–290. MR 943803, DOI 10.1017/S0308210500014669
- 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 1051543, DOI 10.1017/S0022112090002440
- Alan R. Elcrat and Kenneth G. Miller, Rearrangements in steady vortex flows with circulation, Proc. Amer. Math. Soc. 111 (1991), no. 4, 1051–1055. MR 1043409, DOI 10.1090/S0002-9939-1991-1043409-2
- Roger Temam, On the Euler equations of incompressible perfect fluids, J. Functional Analysis 20 (1975), no. 1, 32–43. MR 0430568, DOI 10.1016/0022-1236(75)90052-x
- Bruce Turkington, On steady vortex flow in two dimensions. I, II, Comm. Partial Differential Equations 8 (1983), no. 9, 999–1030, 1031–1071. MR 702729, DOI 10.1080/03605308308820293
- Bruce Turkington, On steady vortex flow in two dimensions. I, II, Comm. Partial Differential Equations 8 (1983), no. 9, 999–1030, 1031–1071. MR 702729, DOI 10.1080/03605308308820293
- 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 1023732, DOI 10.1017/S0022112089002533
- G. Wolansky, Existence, uniqueness, and stability of stationary barotropic flow with forcing and dissipation, Comm. Pure Appl. Math. 41 (1988), no. 1, 19–46. MR 917123, DOI 10.1002/cpa.3160410104
Additional Information
- Takahiro Nishiyama
- Affiliation: Department of Mathematics, Keio University, Yokohama 223–8522, Japan
- Email: nisiyama@math.keio.ac.jp
- Received by editor(s): April 15, 1999
- Published electronically: August 28, 2000
- Communicated by: David S. Tartakoff
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1800232