粘性系数依赖于密度的一维可压等熵Navier-Stokes方程自由边值问题的正则性

Regularity of Solutions to a Free Boundary Problem of 1D Compressible Isentropic Navier-Stokes Equations with Density-dependent Viscosity

研究了一维可压等熵Navier-Stokes方程自由边值问题的正则性.在利用H1中已知结果的基础上,采用能量方法,运用嵌入定理以及精细的插值不等式解决了由于解的高阶偏导导致的复杂估计问题.

The regularity of solutions to a free boundary problem of 1 D compressible isentropic Navier-Stokes equations with density-dependent viscosity is studied. By using the energy method, the embedding theorem and the delicate interpolation techniques on the basis of the known results in H^1 , and the regularity of solutions to a free boundary problem of 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity is established. The mathematical difficulties caused by the higher order of partial derivatives in the proof of the regularity of solutions are solved.