论文标题
关于保护法的独特性解决方案的独特性
On the uniqueness of solutions to hyperbolic systems of conservation laws
论文作者
论文摘要
对于一般的保护法系统，我们表明，属于适当的BESOV空间的耗散弱解决方案$ b^{α，\ infty} _q $并满足单方面结合条件在耗散溶液类中是独一无二的。指数$α> 1/2 $是通用的，与非线性的性质无关，而BESOV规律性仅在系统以适当的变量表示时才在空间中施加。该证明利用换向器估计值，该估算允许将相对熵方法扩展到所需的规律性设置。研究了弹性，浅水磁流失动力学和等质欧拉的系统，从而恢复了后者的最新结果。此外，本文探讨了由色谱研究中的研究动机的三角系统，并构建了一个明确的解决方案，该解决方案未能是Lipschitz，但满足了所提供的独特性结果的条件。
For general hyperbolic systems of conservation laws we show that dissipative weak solutions belonging to an appropriate Besov space $B^{α,\infty}_q$ and satisfying a one-sided bound condition are unique within the class of dissipative solutions. The exponent $α>1/2$ is universal independently of the nature of the nonlinearity and the Besov regularity need only be imposed in space when the system is expressed in appropriate variables. The proof utilises a commutator estimate which allows for an extension of the relative entropy method to the required regularity setting. The systems of elasticity, shallow water magnetohydrodynamics, and isentropic Euler are investigated, recovering recent results for the latter. Moreover, the article explores a triangular system motivated by studies in chromatography and constructs an explicit solution which fails to be Lipschitz, yet satisfies the conditions of the presented uniqueness result.
