粘性项依赖于密度的完全Navier-Stokes方程强解的存在唯一性

The Existence and Uniqueness of Strong Solution for the Density-dependent Full Navier-Stokes Equation

对粘性项依赖于密度的完全Navier-Stokes方程进行了研究,在Rn(n=2,3)中一个边界光滑的区域Ω上讨论该系统的.初始密度满足一个兼容性条件下,本文分别证明了具热源和不具热源时,该系统的强解的存在唯一性.本文所有方法是迭代手法,该方法主要利用线性化系统强解的存在性,然后构造原始系统的迭代系统,根据迭代系统的一致估计,最终通过迭代解序列"函数值变化的一致有界性",得到迭代解序列自然收敛.从而避免了繁琐的紧性讨论.值得一提的是我们的初始密度容许在Ω的一个子集上是真空的.

In this paper,the density-dependent full Navier-Stokes equations are discussed in ΩRn（n=2,3） with smooth boundary.And the existence and the uniqueness strong solution for this system with heat sources or without heat sources are obtained,in condition that the initial density satisfies the compatibility.As methods,the iterative methods are introduced.This method mainly use the existence of strong solution for linearized system.Then by the initial system,the iterative system is constructed,and the uniform estimates are gotten from the iterative system.Finally,for the boundary of the sequences for the iterative solution,the convergence can naturally be concluded.And the complex compact discussion is avoided.Furthermore,the vacuum of initial density may be allowed.