In this paper, we numerically study a class of solutions with spiraling singularities in vorticity for two-dimensional, inviscid, compressible Euler systems, where the initial data have an algebraic singularity in vorticity at the origin. These are different from the multi-dimensional Riemann problems widely studied in the literature. Our computations provide numerical evidence of the existence of initial value problems with multiple solutions, thus revealing a fundamental obstruction toward the well-posedness of the governing equations. The compressible Euler equations are solved using the positivity-preserving discontinuous Galerkin method.

中文翻译：

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二维可压缩等熵欧拉方程非唯一性的数值研究

在本文中，我们数值研究了二维、无粘性、可压缩欧拉系统的一类涡量螺旋奇点解，其中初始数据在原点处具有涡量代数奇点。这些不同于文献中广泛研究的多维黎曼问题。我们的计算提供了具有多个解的初值问题存在的数值证据，从而揭示了控制方程适定性的基本障碍。可压缩欧拉方程使用保正性不连续伽辽金方法求解。