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arXiv · 2311.12087

Global Existence to a Class of Triangular Block Matrix Cross Diffusion Systems and the Spectral Gap Condition

Dung Le
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Abstract

We study the global existence of classical solutions to cross diffusion systems of $m$ equations on $N$-dimensional domains ($m,N\ge2$). The diffusion matrix is a triangular block matrix with coupled entries. We establish that the $W^{1,p}$ norm of solutions for some $p>N$ does not blow up in finite time so that the results in \cite{Am2} is applicable. We will also show that the spectral gap condition in \cite{dlebook,dlebook1} can be relaxed via a new result on BMO norms in \cite{dleBMO}.

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Dung Le. 2023-11-20. Global Existence to a Class of Triangular Block Matrix Cross Diffusion Systems and the Spectral Gap Condition. https://arxiv.org/abs/2311.12087

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