• Previous Article
    Large BV solutions to Euler equations in the isothermal self-gravitating gases with damping
  • CPAA Home
  • This Issue
  • Next Article
    Three nontrivial solutions for periodic problems with the $p$-Laplacian and a $p$-superlinear nonlinearity
July  2009, 8(4): 1439-1450. doi: 10.3934/cpaa.2009.8.1439

Uniqueness of 2-D compressible vortex sheets

1. 

CNRS, Université Lille 1 and Team Project SIMPAF of INRIA Lille Nord Europe, Laboratoire Paul Painlevé, Bâtiment M2, Cité Scientifique, 59655 VILLENEUVE D'ASCQ CEDEX, France

2. 

Dipartimento di Matematica, Facoltà di Ingegneria, Università di Brescia, Via Valotti, 9, 25133 Brescia, Italy

Received  June 2008 Revised  November 2008 Published  March 2009

We consider compressible vortex sheets for the isentropic Euler equations of gas dynamics in two space dimensions. Under a supersonic condition that precludes violent instabilities, in previous papers [3, 4] we have studied the linearized stability and proved the local existence of piecewise smooth solutions to the nonlinear problem. This is a free boundary nonlinear hyperbolic problem with two main difficulties: the free boundary is characteristic, and the so-called Lopatinskii condition holds only in a weak sense, which yields losses of derivatives. In the present paper we prove that sufficiently smooth solutions are unique.
Citation: Jean-françois Coulombel, Paolo Secchi. Uniqueness of 2-D compressible vortex sheets. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1439-1450. doi: 10.3934/cpaa.2009.8.1439
[1]

Tung Chang, Gui-Qiang Chen, Shuli Yang. On the 2-D Riemann problem for the compressible Euler equations II. Interaction of contact discontinuities. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 419-430. doi: 10.3934/dcds.2000.6.419

[2]

Volker Elling. Compressible vortex sheets separating from solid boundaries. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 6781-6797. doi: 10.3934/dcds.2016095

[3]

Xuanji Jia, Yong Zhou. Regularity criteria for the 3D MHD equations via partial derivatives. II. Kinetic and Related Models, 2014, 7 (2) : 291-304. doi: 10.3934/krm.2014.7.291

[4]

Claude Bardos, E. S. Titi. Loss of smoothness and energy conserving rough weak solutions for the $3d$ Euler equations. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 185-197. doi: 10.3934/dcdss.2010.3.185

[5]

Zineb Hassainia, Taoufik Hmidi. Steady asymmetric vortex pairs for Euler equations. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1939-1969. doi: 10.3934/dcds.2020348

[6]

Alessandro Morando, Yuri Trakhinin, Paola Trebeschi. On local existence of MHD contact discontinuities. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 289-313. doi: 10.3934/dcdss.2016.9.289

[7]

Young-Pil Choi. Compressible Euler equations interacting with incompressible flow. Kinetic and Related Models, 2015, 8 (2) : 335-358. doi: 10.3934/krm.2015.8.335

[8]

Shuxing Chen, Gui-Qiang Chen, Zejun Wang, Dehua Wang. A multidimensional piston problem for the Euler equations for compressible flow. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 361-383. doi: 10.3934/dcds.2005.13.361

[9]

Qing Chen, Zhong Tan. Time decay of solutions to the compressible Euler equations with damping. Kinetic and Related Models, 2014, 7 (4) : 605-619. doi: 10.3934/krm.2014.7.605

[10]

Jianwei Yang, Dongling Li, Xiao Yang. On the quasineutral limit for the compressible Euler-Poisson equations. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022020

[11]

Quentin Chauleur. The isothermal limit for the compressible Euler equations with damping. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022059

[12]

Robin Ming Chen, Feimin Huang, Dehua Wang, Difan Yuan. On the stability of two-dimensional nonisentropic elastic vortex sheets. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2519-2533. doi: 10.3934/cpaa.2021083

[13]

Jianwei Yang, Ruxu Lian, Shu Wang. Incompressible type euler as scaling limit of compressible Euler-Maxwell equations. Communications on Pure and Applied Analysis, 2013, 12 (1) : 503-518. doi: 10.3934/cpaa.2013.12.503

[14]

Zhilei Liang. Convergence rate of solutions to the contact discontinuity for the compressible Navier-Stokes equations. Communications on Pure and Applied Analysis, 2013, 12 (5) : 1907-1926. doi: 10.3934/cpaa.2013.12.1907

[15]

Matthias Eller. Loss of derivatives for hyperbolic boundary problems with constant coefficients. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1347-1361. doi: 10.3934/dcdsb.2018154

[16]

Hong Cai, Zhong Tan. Stability of stationary solutions to the compressible bipolar Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 4677-4696. doi: 10.3934/dcds.2017201

[17]

Harish S. Bhat, Razvan C. Fetecau. Lagrangian averaging for the 1D compressible Euler equations. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 979-1000. doi: 10.3934/dcdsb.2006.6.979

[18]

Ruiying Wei, Yin Li, Zheng-an Yao. Global existence and convergence rates of solutions for the compressible Euler equations with damping. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 2949-2967. doi: 10.3934/dcdsb.2020047

[19]

Haigang Li, Jiguang Bao. Euler-Poisson equations related to general compressible rotating fluids. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1085-1096. doi: 10.3934/dcds.2011.29.1085

[20]

Paola Goatin, Philippe G. LeFloch. $L^1$ continuous dependence for the Euler equations of compressible fluids dynamics. Communications on Pure and Applied Analysis, 2003, 2 (1) : 107-137. doi: 10.3934/cpaa.2003.2.107

2020 Impact Factor: 1.916

Metrics

  • PDF downloads (74)
  • HTML views (0)
  • Cited by (12)

Other articles
by authors

[Back to Top]