论文标题
经典解决方案对浅水的粘性圣人系统的真空无边界问题的良好性
Well-posedness of classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow waters
论文作者
论文摘要
我们建立了经典解决方案的局部良好性，以解决严格从不可压缩的Navier-Stokes系统中衍生出的粘性圣人系统的真空无界边界问题，并通过Gerbeau-Perthame具有移动的自由表面。我们的解决方案（高度和速度）是平滑的（解决方案都满足了方程式尖端），尽管高度作为到真空边界的距离的奇异性都脱离了移动边界。该证明是建立在一些与移动真空边界附近退化性相关的一些新的高阶加权能量功能和加权估计上建立的。
We establish the local-in-time well-posedness of classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow waters derived rigorously from incompressible Navier-Stokes system with a moving free surface by Gerbeau-Perthame. Our solutions (the height and velocity) are smooth (the solutions satisfy the equations point-wisely) all the way to the moving boundary, although the height degenerates as a singularity of the distance to the vacuum boundary. The proof is built on some new higher-order weighted energy functional and weighted estimates associated to the degeneracy near the moving vacuum boundary.
