A remark on the Cauchy problem of 1D compressible Navier-Stokes equations with density-dependent viscosity coefficients |
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Authors: | Jin-tao Wei Lin He Zhen-hua Guo |
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Affiliation: | 1. Department of College Mathematics Teaching, Longqiao College of Lanzhou Commercial College, Lanzhou, 730101, China 2. CNS and Department of Mathematics, Northwest University, Xi’an, 710069, China
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Abstract: | This paper is concerned with the Cauchy problems of one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefficients. By assuming ρ 0 ∈ L 1(R), we will prove the existence of weak solutions to the Cauchy problems for θ > 0. This will improve results in Jiu and Xin’s paper (Kinet. Relat. Models, 1(2): 313–330 (2008)) in which θ > $tfrac{1} {2} $ is required. In addition, We will study the large time asymptotic behavior of such weak solutions. |
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Keywords: | Cauchy problem compressible flows density-dependent viscosity Coefficients |
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