Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Uniform regularity for the incompressible Navier-Stokes system with variable density and Navier boundary conditions


Author: Xin Xu
Journal: Quart. Appl. Math.
MSC (2010): Primary 35Q35, 76N10, 76N20
DOI: https://doi.org/10.1090/qam/1515
Published electronically: August 28, 2018
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Abstract: We investigate the uniform regularity for the nonhomogeneous incompressible Navier-Stokes system with Navier boundary conditions and the inviscid limit to the Euler system. It is shown that there exists a unique strong solution of the Navier-Stokes equations in an interval of time that is uniform with respect to the viscosity parameter. The uniform estimate in conormal Sobolev spaces is established. Based on the uniform estimate, we show the convergence of the viscous solutions to the inviscid ones in $ L^\infty ([0,T]\times \Omega )$. This improves the result obtained by Ferreira et al. [SIAM J. Math. Anal. Vol. 45, No. 4, (2013), pp. 2576-2595], where $ L^\infty ([0,T],L^2(\Omega ))$ convergence was proved.


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Additional Information

Xin Xu
Affiliation: School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel
Email: xuxinaboy@126.com

DOI: https://doi.org/10.1090/qam/1515
Received by editor(s): December 16, 2017
Received by editor(s) in revised form: July 4, 2018
Published electronically: August 28, 2018
Article copyright: © Copyright 2018 Brown University

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