Revista Matemática Iberoamericana


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Volume 26, Issue 3, 2010, pp. 915–946
DOI: 10.4171/RMI/621

Published online: 2010-12-31

Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities

Qionglei Chen[1], Changxing Miao[2] and Zhifei Zhang[3]

(1) Institute of Applied Physics and Computational Mathematics, Beijing, China
(2) Institute of Applied Physics and Computational Mathematics, Beijing, China
(3) Peking University, Beijing, China

In this paper, we prove the local well-posedness in critical Besov spaces for the compressible Navier-Stokes equations with density dependent viscosities under the assumption that the initial density is bounded away from zero.

Keywords: Compressible Navier-Stokes equations, Besov spaces, Bony’s paraproduct, Fourier localization

Chen Qionglei, Miao Changxing, Zhang Zhifei: Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities. Rev. Mat. Iberoamericana 26 (2010), 915-946. doi: 10.4171/RMI/621