Analysis and Probability Seminar

Abstract: Used by Koch--Tataru for Navier--Stokes equations, the theory of tent spaces turns out to be useful to deal with evolution equations allowing distributional initial data, due to its strong connection with harmonic analysis as shown in the eminent works of Fefferman--Stein and Coifman--Meyer--Stein. In this talk, we use tent spaces to investigate well-posedness of Cauchy problems of linear parabolic equations with time-independent, uniformly elliptic, bounded measurable complex coefficients, with various possible sorts of source terms. The initial data can be tempered distributions taken in homogeneous Hardy--Sobolev spaces $\Dot{H}^{s,p}$ with $-1<s<1$. The talk is based on a series of joint works with Pascal Auscher.