Osaka Journal of Mathematics

Uniform boundedness of the radially symmetric solutions of the Navier-Stokes equations for isentropic compressible fluids

Jishan Fan, Song Jiang, and Guoxi Ni

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We study the isentropic compressible Navier-Stokes equations with radially symmetric data and non-negative initial density in an annular domain. We prove the global existence of strong solutions for any $\gamma\geq 1$. Moreover, we obtain the uniform in time $L^{\infty}$-boundedness of the density and $H^{1}$-boundedness of the velocity, improving therefore the corresponding result in [2], where the condition $\gamma\geq 2$ is required to guarantee the existence.

Article information

Osaka J. Math., Volume 46, Number 3 (2009), 863-876.

First available in Project Euclid: 26 October 2009

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Zentralblatt MATH identifier

Primary: 76N15: Gas dynamics, general 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35Q35: PDEs in connection with fluid mechanics 35M20


Fan, Jishan; Jiang, Song; Ni, Guoxi. Uniform boundedness of the radially symmetric solutions of the Navier-Stokes equations for isentropic compressible fluids. Osaka J. Math. 46 (2009), no. 3, 863--876.

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