论文标题
不可压缩流体动力学的最大耗散溶液
Maximal dissipative solutions for incompressible fluid dynamics
论文作者
论文摘要
我们介绍了一类等温通用系统的最大耗散解决方案的新概念。在某些假设下，我们表明，只要较大的耗散解决方案是非空的，就可以很好地提出最大耗散溶液。将此结果应用于Navier-Stokes和Euler方程，我们推断了这些系统的最大耗散解决方案的全球适应性。只要弱解决方案继承了足够的规律性以独一无二，最大耗散解决方案的概念与弱解决方案的概念一致。
We introduce the new concept of maximal dissipative solutions for a general class of isothermal GENERIC systems. Under certain assumption, we show that maximal dissipative solutions are well posed as long as the bigger class of dissipative solutions is non-empty. Applying this result to the Navier--Stokes and Euler equations, we infer global well-posedness of maximal dissipative solutions for these systems. The concept of maximal dissipative solutions coincides with the concept of weak solutions as long as the weak solutions inherits enough regularity to be unique.
