Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model. (15th December 2013)

• Record Type: Journal Article
• Authors: Xie, Weijun; Zhang, Yinghui; Xiao, Yuandong; Wei, Wei
• Other Names: Govinder K. S. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-12-15
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/391056
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We are concerned with a 3D chemotaxis model arising from biology, which is a coupled hyperbolic-parabolic system. We prove the global existence of a strong solution when H 2 -norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, L 1 -norm of the initial perturbation is bounded; the optimal convergence rates are also obtained for such a solution. The proofs are obtained by combining spectral analysis with energy methods.