The strong relaxation limit of the multidimensional Euler equations

Chunjin Lin (1) , Jean-François Coulombel (2)

1 College of Computer and Information Engineering [Hohai]
2 SIMPAF - SImulations and Modeling for PArticles and Fluids

This paper is devoted to the analysis of global smooth solutions to the multidimensional isentropic Euler equations with sti relaxation. We show that the asymptotic behavior of the global smooth solution is governed by the porous media equation as the relaxation time tends to zero. The results are proved by combining some classical energy estimates with the so-called Shizuta-Kawashima condition.

Mots clés: Global existence; Initial value problem; Euler equations; Porous media equation; Relaxation

Domaines: Equations aux dérivées partielles [math.AP]

Chunjin Lin, Jean-François Coulombel. The strong relaxation limit of the multidimensional Euler equations. Nonlinear Differential Equations and Applications, 2013, 20 (3), pp.447-461. ⟨10.1007/s00030-012-0159-0⟩. ⟨hal-00622938⟩