Large time behavior of solutions to the compressible Navier-Stokes equations with potential force

作者：Wang, Wenjun^*

来源：Journal of Mathematical Analysis and Applications, 2015, 423(2): 1448-1468.

DOI：10.1016/j.jmaa.2014.10.050

• Navier-Stokes equations
• Potential force
• Global existence
• Time decay rates

The compressible Navier-Stokes equation with a potential external force is considered in R-3 in the present paper. Under the smallness assumption on both the external force and the initial perturbation of the stationary solution in some Sobolev spaces, the existence theory of global solutions to the stationary profile is established. Furthermore, when the H-s norm (s is an element of (0, 1/2)) of initial perturbation is finite, we obtain the optimal time decay rates of the solutions in L-2-norm. As a corollary, the L-p-L-q (3/2 < p <= 2) type of the decay rates follows without requiring that the L-p norm of initial perturbation is small.

• 出版日期2015-3-15
• 单位上海理工大学