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| Expansion of a Wedge of Gas into Vacuum with Small Angle |
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Citation： |
J. Ge,W. C. Sheng.Expansion of a Wedge of Gas into Vacuum with Small Angle[J].Chinese Annals of Mathematics B,2016,37(3):395~404 |
| Page view： 1474
Net amount： 1135 |
Authors： |
J. Ge; W. C. Sheng |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11371240), Shanghai Municipal Education
Commission of Scientific Research Innovation Project (No.11ZZ84),
the Fundamental Research Funds for the Central Universities
(No.15CX02074A) and the grant of the First-Class Discipline of
Universities in Shanghai''. |
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| Abstract： |
In this paper, the authors consider the expansion problem of a wedge
of gas into vacuum for the two-dimensional Euler equations in
isothermal flow. By the bootstrapping argument, they prove the
global existence of the smooth solution through the direct method in
the case
$0<\theta\leq\ov{\theta}=\arctan{\frac{1}{\sqrt{{2+\sqrt{5}}}}}$,
where $\theta$ is the half angle of the wedge. Furthermore, they get
the uniform $ C^{ 1,1}$ estimates of the solution to the expansion
problem. |
Keywords： |
Hyperbolic partial differential equation, 2D Riemann problem,
Rarefaction wave, Isothermal flow |
Classification： |
35L65, 35L80, 35R35, 35L60, 35L50 |
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