# American Institute of Mathematical Sciences

June  2018, 11(3): 469-490. doi: 10.3934/krm.2018021

## Incompressible Limit of isentropic Navier-Stokes equations with Navier-slip boundary

 Institute of Mathematics, Hunan University, Changsha 410082, China

Received  April 2017 Revised  July 2017 Published  March 2018

Fund Project: The research was supported by NSFC (Grant Nos.11501187, 11771132) and Fundamental Research Funds for the Central Universities.

This paper concerns the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for isentropic fluids in a bounded domain with a Navier-slip boundary condition. In [2], it has been proved that if the velocity is imposed the homogeneous Dirichlet boundary condition, as the Mach number goes to 0, the velocity of the compressible flow converges strongly in $L^2$ under the geometrical assumption (H) on the domain. We justify the same strong convergence when the slip length in the Navier condition is the reciprocal of the square root of the Mach number.

Citation: Linjie Xiong. Incompressible Limit of isentropic Navier-Stokes equations with Navier-slip boundary. Kinetic & Related Models, 2018, 11 (3) : 469-490. doi: 10.3934/krm.2018021
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