March  2003, 2(1): 107-137. doi: 10.3934/cpaa.2003.2.107

$L^1$ continuous dependence for the Euler equations of compressible fluids dynamics

1. 

Centre de Mathématiques Appliquées, & Centre National de la Recherche Scientifique, UMR. 7641, Ecole Polytechnique, 91128 Palaiseau Cedex, France

2. 

Centre de Mathématiques Appliquées, and Centre National de la Recherche Scientifique, UMR. 7641, Ecole Polytechnique, 91128 Palaiseau Cedex, France

Received  April 2002 Revised  September 2002 Published  December 2002

We prove the $L^1$ continuous dependence of entropy solutions for the $2 \times 2$ (isentropic) and the $3\times 3$ (non-isentropic) systems of inviscid fluid dynamics in one-space dimension. We follow the approach developed by the second author for solutions with small total variation to general systems of conservation laws in [11, 14]. For the systems of fluid dynamics under consideration here, our estimates are more precise and we cover entropy solutions with large total variation.
Citation: 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
[1]

Christophe Cheverry, Mekki Houbad. A class of large amplitude oscillating solutions for three dimensional Euler equations. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1661-1697. doi: 10.3934/cpaa.2012.11.1661

[2]

Hongyun Peng, Lizhi Ruan, Changjiang Zhu. Convergence rates of zero diffusion limit on large amplitude solution to a conservation laws arising in chemotaxis. Kinetic and Related Models, 2012, 5 (3) : 563-581. doi: 10.3934/krm.2012.5.563

[3]

Rinaldo M. Colombo, Francesca Monti. Solutions with large total variation to nonconservative hyperbolic systems. Communications on Pure and Applied Analysis, 2010, 9 (1) : 47-60. doi: 10.3934/cpaa.2010.9.47

[4]

Zhenhua Guo, Wenchao Dong, Jinjing Liu. Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids. Communications on Pure and Applied Analysis, 2019, 18 (4) : 2133-2161. doi: 10.3934/cpaa.2019096

[5]

Zefu Feng, Changjiang Zhu. Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3069-3097. doi: 10.3934/dcds.2019127

[6]

Serhiy Yanchuk, Leonhard Lücken, Matthias Wolfrum, Alexander Mielke. Spectrum and amplitude equations for scalar delay-differential equations with large delay. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 537-553. doi: 10.3934/dcds.2015.35.537

[7]

JÓzsef Balogh, Hoi Nguyen. A general law of large permanent. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5285-5297. doi: 10.3934/dcds.2017229

[8]

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

[9]

Giuseppe Maria Coclite, Lorenzo Di Ruvo. A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1247-1282. doi: 10.3934/dcds.2017052

[10]

Teng Wang, Yi Wang. Large-time behaviors of the solution to 3D compressible Navier-Stokes equations in half space with Navier boundary conditions. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2811-2838. doi: 10.3934/cpaa.2021080

[11]

Guy Métivier, Kevin Zumbrun. Large-amplitude modulation of periodic traveling waves. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022070

[12]

Jean Dolbeault, Giuseppe Toscani. Fast diffusion equations: Matching large time asymptotics by relative entropy methods. Kinetic and Related Models, 2011, 4 (3) : 701-716. doi: 10.3934/krm.2011.4.701

[13]

Zhong Tan, Yong Wang, Fanhui Xu. Large-time behavior of the full compressible Euler-Poisson system without the temperature damping. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1583-1601. doi: 10.3934/dcds.2016.36.1583

[14]

Yachun Li, Xucai Ren. Non-relativistic global limits of the entropy solutions to the relativistic Euler equations with $\gamma$-law. Communications on Pure and Applied Analysis, 2006, 5 (4) : 963-979. doi: 10.3934/cpaa.2006.5.963

[15]

Zengjing Chen, Weihuan Huang, Panyu Wu. Extension of the strong law of large numbers for capacities. Mathematical Control and Related Fields, 2019, 9 (1) : 175-190. doi: 10.3934/mcrf.2019010

[16]

Weike Wang, Xin Xu. Large time behavior of solution for the full compressible navier-stokes-maxwell system. Communications on Pure and Applied Analysis, 2015, 14 (6) : 2283-2313. doi: 10.3934/cpaa.2015.14.2283

[17]

Julián López-Gómez. Uniqueness of radially symmetric large solutions. Conference Publications, 2007, 2007 (Special) : 677-686. doi: 10.3934/proc.2007.2007.677

[18]

Ling-Jun Wang. The dynamics of small amplitude solutions of the Swift-Hohenberg equation on a large interval. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1129-1156. doi: 10.3934/cpaa.2012.11.1129

[19]

Freddy Dumortier. Sharp upperbounds for the number of large amplitude limit cycles in polynomial Lienard systems. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1465-1479. doi: 10.3934/dcds.2012.32.1465

[20]

Walter A. Strauss, Masahiro Suzuki. Large amplitude stationary solutions of the Morrow model of gas ionization. Kinetic and Related Models, 2019, 12 (6) : 1297-1312. doi: 10.3934/krm.2019050

2021 Impact Factor: 1.273

Metrics

  • PDF downloads (71)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]