The expansion of a wedge of gas into vacuum with small angle in two-dimensional isothermal flow

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 $0 < \theta \leqslant \bar \theta = \arctan \tfrac{1}{{\sqrt {2 + \sqrt 5 } }}$, where θ 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

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