Global well-posedness and zero diffusion limit of classical solutions to 3D conservation laws arising in chemotaxis

作者：Peng, Hongyun^*; Wen, Huanyao; Zhu, Changjiang

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2014, 65(6): 1167-1188.

DOI：10.1007/s00033-013-0378-1

• Conservation laws
• Chemotaxis
• Large amplitude solution
• Convergence rate
• Zero diffusion limit

In this paper, we study the existence of global classical solutions and the vanishing diffusion limit of a 3D conservation laws derived from the well-known Keller-Segel model. First, we establish the global well-posedness of classical solutions to the Cauchy problem for the model with smooth initial data which is of small L (2) norm, together with some a priori estimates uniform for t and . Then, we investigate the zero diffusion limit and get the global well-posedness of classical solutions to the Cauchy problem for the non-diffusive model. Finally, we derive the convergence rate of the model toward the non-diffusive model. It is shown that the convergence rate in L (a) norm is of the order . It should be noted that the initial data are small in L (2)-norm but can be of large oscillations with constant state at far field. As a byproduct, we improve the corresponding result on the well-posedness of the non-diffusive model which requires small oscillations.

• 出版日期2014-12
• 单位华中师范大学