en fr Study of weak infinite energy solutions for a non local transport equation Etude de la régularité des solutions faibles d’énergie infinie d’une équation de transport non locale Report as inadecuate




en fr Study of weak infinite energy solutions for a non local transport equation Etude de la régularité des solutions faibles d’énergie infinie d’une équation de transport non locale - Download this document for free, or read online. Document in PDF available to download.

1 LAMA - Laboratoire d-Analyse et de Mathématiques Appliquées

Abstract : In this thesis, we adress the study of weak infinite energy solutions for the critical dissipative quasi geostrophic SQG equation. We also study a 1D transport equation with non local velocity. More precisely, we consider the SQG equation equation with data in Morrey-Camapanto type spaces and the other equation in a weighted Lebesgue spaces. Both spaces generate infinite energy solutions. Regarding the 1D equation with non local velocity, the existence of weak Morrey solutions is not easy to obtain, this is due to the fact that the non linearity is not written in a divergence form. Nevertheless, we are able to adress the study this 1D equation in a weigted Lebesgue space and this also provides infinite energy solutions. In a first part, we show that for any initial data lying in a Morrey-Campanato space for large enough oscillations, we have global existence of weak solutions. The proof is based on the study of the truncated equation on a ball of radius $R>0$ centered at the origin associated with a truncated et regularized initial data by making a convolution with a standard mollifer. We obtain emph{a priori} estimates that give rise to an energy inequality. Then, we treat the case of small oscillations, namely $0



Author: Omar Lazar -

Source: https://hal.archives-ouvertes.fr/



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