A remark on regularity of 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity |
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Authors: | Yuming Qin Lan Huang |
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Affiliation: | a Department of Applied Mathematics, Donghua University, Shanghai 201620, PR China b College of Information Science and Technology, Donghua University, Shanghai 201620, PR China c Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, PR China |
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Abstract: | In this paper, we consider one-dimensional compressible isentropic Navier-Stokes equations with the viscosity depending on density and with the free boundary. The viscosity coefficient μ is proportional to ρθ with θ>0, where ρ is the density. The existence, uniqueness, regularity of global weak solutions in H1([0,1]) have been established by Xin and Yao in [Z. Xin, Z. Yao, The existence, uniqueness and regularity for one-dimensional compressible Navier-Stokes equations, preprint]. Furthermore, under certain assumptions imposed on the initial data, we improve the regularity result obtained in [Z. Xin, Z. Yao, The existence, uniqueness and regularity for one-dimensional compressible Navier-Stokes equations, preprint] by driving some new a priori estimates. |
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Keywords: | Compressible Navier-Stokes equations Viscosity Regularity Vacuum |
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