论文标题
可压缩的Navier-Stokes方程具有异质压力定律
Compressible Navier-Stokes equations with heterogeneous pressure laws
论文作者
论文摘要
本文涉及具有压缩性的Navier-Stokes方程的全球弱解决方案的存在，其压力定律取决于密度以及时间和空间变量$ t $和$ x $。压力上的假设仅包含有关密度变量的局部Lipschitz假设，以及关于额外的时间和空间变量的假设。可以将其视为考虑具有诸如截短病毒假设的物理定律的热传导的Navier-Stokes方程的第一步。本文着重于通过新的正规化和固定点过程以及弱稳定过程的构建，利用了两位第一作者引入的新方法，并仔细研究了与压力相关的适当正则化数量。
This paper concerns the existence of global weak solutions à la Leray for compressible Navier-Stokes equations with a pressure law that depends on the density and on time and space variables $t$ and $x$. The assumptions on the pressure contain only locally Lipschitz assumption with respect to the density variable and some hypothesis with respect to the extra time and space variables. It may be seen as a first step to consider heat-conducting Navier-Stokes equations with physical laws such as the truncated virial assumption. The paper focuses on the construction of approximate solutions through a new regularized and fixed point procedure and on the weak stability process taking advantage of the new method introduced by the two first authors with a careful study of an appropriate regularized quantity linked to the pressure.
