Studies in analyticity for hydrodynamic and chemotaxis models
Time and place
12:30 PM on Thursday, February 21st, 2019; NAC 6/114
Vincent Martinez (Hunter College (CUNY))
Abstract
In their 1987 seminal paper, Foias and Temam established analyticity in both space and time for solutions of the two(2D) and three-dimensional (3D) Navier-Stokes equations (NSE) by developing an energy method now known as the technique of Gevrey-norms, i.e., a norm which characterizes real analyticity of a function. This approach has since become standard for establishing spatial analyticity of solutions to various parabolic-type equations. In this talk, we shed light on the relation between the structure of the equation and its well-posedness theory in various analytic Gevrey-norm regularity classes. We do so in the context of the supercritical SQG equation, the Keller-Segel equation, and a coupled chemotaxis-hydrodynamic model through the notion of “criticality.”
