Existence results for chemotaxis-shallow water system with degenerate viscosity coefficients and initial vacuum. (November 2019)

• Record Type: Journal Article
• Authors: Wang, Zhigang
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 265
• Page End: 293
• Publication Date: 2019-11
• Subjects: primary 35Q35 35Q92 76N10 92C17 -- secondary 35M10 35Q30; Chemotaxis-shallow water system -- Regular solutions -- Initial vacuum -- Degenerate viscosity coefficients; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.06.005
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is concerned with the Cauchy problem of the chemotaxis-shallow water system with degenerate viscosity coefficients. A local existence of the unique regular solution is established when the initial data are arbitrarily large and include vacuum. Moreover, a Beal–Kate–Majda type blow-up criterion is provided.