We discuss L-p integrability estimates for the solution u of the advection-diffusion equation partial derivative(t)u+div(bu) =Delta u, where the velocity field b is an element of (LtLxq)-L-r. We first summarize some classical results proving such estimates for certain ranges of the exponents r and q. Afterwards we prove the optimality of such ranges by means of new original examples
Optimality of integrability estimates for advection-diffusion equations
LV Spinolo
2017
Abstract
We discuss L-p integrability estimates for the solution u of the advection-diffusion equation partial derivative(t)u+div(bu) =Delta u, where the velocity field b is an element of (LtLxq)-L-r. We first summarize some classical results proving such estimates for certain ranges of the exponents r and q. Afterwards we prove the optimality of such ranges by means of new original examplesFile in questo prodotto:
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