Dissipation Enhancement Mechanism Of Couette Flow In Chemotaxis Equation With Consumption

Chemotaxis is a directed response of organisms stimulated by chemicals in the ex-ternal environment,such as the movement of bacteria toward high glucose concentrations during reproduction or away from the toxic substance phenol.In order to understand the evolutionary mechanism of chemotaxis,chemotaxis has been analyzed and mathemati-cally modeled from microscopic and macroscopic perspectives since 1960s.Keller and Segel described the biological chemotaxis from a mathematical point of view using a sys-tem of partial differential equations.This thesis focuses on the effect of Couette flow on the global existence of solu-tions to the following two-dimension Keller-Segel-Navier-Stokes model with a chemical consumption mechanism:where n(x,y,t),c(x,y,t)andν(x,y,t)denote the microbial density,chemical density and fluid velocity,respectively,p is the fluid pressure,T is a bounded domain,and R represents the real number field.This thesis focuses on establishing dissipation-enhanced estimates of the model by an energy approach,and then proves that the solution of the above model does not blow-up in finite time when the Couette flow amplitude is large enough and(?)c(x,y,0)satisfies certain conditions.