论文标题
3D可压缩的Navier-Stokes方程的全局良好性在最大规律性类别中具有自由表面
Global wellposedness of the 3D compressible Navier-Stokes equations with free surface in the maximal regularity class
论文作者
论文摘要
本文涉及Navier-Stokes方程（CNS）的全球良好姿势问题，描述了在三维外部结构域中占用的自由表面的正压压缩流体流动。结合最大$ l_p $ - $ l_q $估计和$ l_p $ - $ l_q $ l_q $ decay decay估算对线性方程的解决方案的衰减估计，我们证明了在时间加权的最大$ l_p $ l_p $ - $ l_q $ $ p> $ p> $ q> $ q> $ q的$ l_q的常规级别中，全球时间解决方案的独特存在，$ q> $ q> $ q>。在太空中。与未约束域中（CNS）的自由边界价值问题的先前结果相比，我们放宽了初始状态的规则性假设，这是使用最大$ L_P $ -L_Q $规则性框架的优势。另一方面，不需要球体的移动边界的平衡状态。据我们所知，本文是（CNS）在外部域中长期解决性问题的第一个结果。
This paper concerns the global well posedness issue of the Navier-Stokes equations (CNS) describing barotropic compressible fluid flow with free surface occupied in the three dimensional exterior domain. Combining the maximal $L_p$-$L_q$ estimate and the $L_p$-$L_q$ decay estimate of solutions to the linearized equations, we prove the unique existence of global in time solutions in the time weighted maximal $L_p$-$L_q$ regularity class for some $p>2$ and $q>3.$ Namely, the solution is bounded as $L_p$ in time and $L_q$ in space. Compared with the previous results of the free boundary value problem of (CNS) in unbounded domains, we relax the regularity assumption on the initial states, which is the advantage by using the maximal $L_p$-$L_q$ regularity framework. On the other hand, the equilibrium state of the moving boundary of the exterior domain is not necessary the sphere. To our knowledge, this paper is the first result on the long time solvability of the free boundary value problem of (CNS) in the exterior domain.
