Optimality of integrability estimates for advection-diffusion equations

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TitleOptimality of integrability estimates for advection-diffusion equations
Publication TypeReport Series
Year of Publication2017
AuthorsBianchini S., Colombo M., Crippa G., Spinolo LV
SeriesIMATI Report Series
Number17-04
Pagination19 p.
Date PublishedFebruary
Place PublishedPavia
PublisherCNR-IMATI
Type of WorkWorking paper
Abstract

We discuss integrability estimates for the solution of an advection-diffusion equation. We first summarize some classical results proving such estimates for certain ranges of the space and time summability of the velocity field. Afterwards we prove the optimality of such ranges by means of new original examples.
KeywordsAdvection-diffusion equation, Duhamel formula, integrability estimates and their optimality, parabolic equations, self-similar solutions
URIhttp://irs.imati.cnr.it/reports/irs17-04
Citation Keyirs17-04
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