Existence of global smooth solutions for euler equations with symmetry |
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| Authors: | Ying Lung-an Yang Tong Zhu Changjiag |
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| Affiliation: | 1. Department of Mathematics , peking University , China;2. Department of Mathematics , City University of Hong Kong , Hong Kong;3. Department of Mathematics , Wuhan Institute of Physics and Mathematics , City Universitiy of Hong Kong, Hong KongChinese Academy of Sciences |
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| 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 smoothe solutions for the initial-boundary value problem ofo Euler equtions satisfying γ law with damping and exisymmetry, 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 C 1 norm of the solutions. |
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