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 free boundary. The viscosity coefficient μ is proportional to ρθ with 0<θ<1, where ρ is the density. The existence and uniqueness of global weak solutions in H1([0,1]) have been established in [S. Jiang, Z. Xin, P. Zhang, Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity, Methods Appl. Anal. 12 (2005) 239-252]. We will establish the regularity of global solution under certain assumptions imposed on the initial data by deriving some new a priori estimates. |
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Keywords: | Compressible Navier-Stokes equations Viscosity Regularity Vacuum |
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