论文标题
对双曲线保护法的能量变化解决方案存在
Existence of energy-variational solutions to hyperbolic conservation laws
论文作者
论文摘要
我们介绍了针对双曲线保护法的能量变化解决方案的概念。本质上，这些能量变化的解决方案满足了弱的唯一原理和半流量的特性，并且解决方案集合均凸出且弱星封闭。通过在某些假设下的合适的时间欺骗方案证明了能量变化解决方案的存在。这一普遍的结果产生了对理想不可压缩流体的磁流体动力方程的能量变化溶液，以及在不可压缩和可压缩的情况下的欧拉方程。此外，我们表明，对欧拉方程的能量变化溶液与耗散性弱解决方案一致。
We introduce the concept of energy-variational solutions for hyperbolic conservation laws. Intrinsically, these energy-variational solutions fulfill the weak-strong uniqueness principle and the semi-flow property, and the set of solutions is convex and weakly-star closed. The existence of energy-variational solutions is proven via a suitable time-discretization scheme under certain assumptions. This general result yields existence of energy-variational solutions to the magnetohydrodynamical equations for ideal incompressible fluids and to the Euler equations in both the incompressible and the compressible case. Moreover, we show that energy-variational solutions to the Euler equations coincide with dissipative weak solutions.
