Cauchy problem with general discontinuous initial data along a smooth curve for 2-d Euler system |
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Authors: | Shuxing Chen Dening Li |
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Affiliation: | 1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China;2. Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA |
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Abstract: | We study the Cauchy problems for the isentropic 2-d Euler system with discontinuous initial data along a smooth curve. All three singularities are present in the solution: shock wave, rarefaction wave and contact discontinuity. We show that the usual restrictive high order compatibility conditions for the initial data are automatically satisfied. The local existence of piecewise smooth solution containing all three waves is established. |
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Keywords: | 35L60 35L65 35L67 76L05 |
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