Existence of global smooth solutions for euler equations with symmetry

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1361-1387
Journal / PublicationCommunications in Partial Differential Equations
Volume22
Issue number7-8
Publication statusPublished - 1997

Abstract

Eventhough existence of global smooth solutions for one dimensional quasilinear hyperbolic systems has been well established, much less is known about the corresponding results for higher dimensional cases. In this paper, we study the existence of global smooth solutions for the initial-boundary value problem of Euler equtions satisfying γ-law with damping and axisymmetry, or spherical symmetry. When the damping is strong enough, we give some sufficient conditions for existence of global smooth solutions as 1 <γ <5/3 and 5/3 <γ <3. The proof is based on technical estimation of the C1 norm of the solutions.

Citation Format(s)

Existence of global smooth solutions for euler equations with symmetry. / Ying, Lung-An; Yang, Tong; Zhu, Changjiang.

In: Communications in Partial Differential Equations, Vol. 22, No. 7-8, 1997, p. 1361-1387.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review