论文标题
与真空的非均匀不可压缩的不对称流体的独特全局可溶性
The unique global solvability of the nonhomogeneous incompressible asymmetric fluids with vacuum
论文作者
论文摘要
本文涉及尺寸$ d = 2,3 $的不均匀不可压缩的不对称流体方程。目的是证明系统的唯一全局可溶解性，只有有界的非负初始密度和$ h^{1} $初始速度。我们首先在2-D中使用大数据构建解决方案的全局存在。接下来，我们为任意大数据和全球及时的局部解决方案建立本地解决方案的存在。最后，解决方案的独特性在对其规律性的相当柔和的假设中得到了证明。特别是，允许初始真空。
The present paper deals with the nonhomogeneous incompressible asymmetric fluids equations in dimension $d= 2,3$. The aim is to prove the unique global solvability of the system with only bounded nonnegative initial density and $H^{1}$ initial velocities. We first construct the global existence of the solution with large data in 2-D. Next, we establish the existence of local in time solution for arbitrary large data and global in time for some smallness conditions in 3-D. Finally, the uniqueness of the solution is proved under quite soft assumptions about its regularity through a Lagrangian approach. In particular, the initial vacuum is allowed.
