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On the vanishing viscosity limit for a 3-D system arising from the Keller-Segel model |
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| Authors: | Linlin Meng Wen-Qing Xu Shu Wang |
| Institution: | 1. Department of Applied Mathematics, College of Applied Sciences, Beijing University of Technology, Beijing, China;2. Department of Applied Mathematics, College of Applied Sciences, Beijing University of Technology, Beijing, China
Department of Mathematics and Statistics, California State University, Long Beach, California |
| Abstract: | In this paper, we consider the vanishing viscosity limit problem for a system arising from the Keller-Segel equations in three space dimensions. First, we construct an accurate approximate solution that incorporates the effects of boundary layers. Then, we prove the structural stability of the approximate solution as the chemical diffusion coefficient tends to zero. Our approach is based on the method of matched asymptotic expansions of singular perturbation theory and the classical energy estimates. |
| Keywords: | boundary layer phenomenon chemotaxis energy estimates Keller-Segel model matched asymptotic expansions |