论文标题
MHD方程耗散解决方案的规律性理论
Regularity theory for the dissipative solutions of the MHD equations
论文作者
论文摘要
我们在这里研究Caffarelli，Kohn和Nirenberg的部分规律性理论的新概括，用于MHD方程的弱解决方案。实际上，在此框架中，通常会要求在压力p上进行一些假设（例如，在$ l q t l 1 x中使用q> 1 x），然后在时间和空间变量中进行局部h {Ö} lder规律性，以便在小社区中获得弱解决方案。通过引入耗散溶液的概念，我们削弱了压力上的假设（我们只假定$ d中的p $ \），我们将在空间变量中获得h {Ö} lder的规律性。
We study here a new generalization of Caffarelli, Kohn and Nirenberg's partial regularity theory for weak solutions of the MHD equations. Indeed, in this framework some hypotheses on the pressure P are usually asked (for example P $\in$ L q t L 1 x with q > 1) and then local H{ö}lder regularity, in time and space variables, for weak solutions can be obtained over small neighborhoods. By introducing the notion of dissipative solutions, we weaken the hypothesis on the pressure (we will only assume that P $\in$ D) and we will obtain H{ö}lder regularity in the space variable for weak solutions.
