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On local well-posedness of logarithmic inviscid regularizations of generalized SQG equations in borderline Sobolev spaces

2021
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Communications on Pure and Applied Analysis
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<p style='text-indent:20px;'>This paper studies a family of generalized surface quasi-geostrophic (SQG) equations for an active scalar <inline-formula><tex-math id="M1">\begin{document}$ \theta $\end{document}</tex-math></inline-formula> on the whole plane whose velocities have been mildly regularized, for instance, logarithmically. The well-posedness of these regularized models in borderline Sobolev regularity have previously been studied by D. Chae and J. Wu when the velocity

doi:10.3934/cpaa.2021169
fatcat:iyxfp54bgzfjhdp4pvvrhlwq5i