标题： 一类三角块矩阵交叉扩散系统的全局存在性及谱间隙条件 显示英文标题

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

摘要： 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. 我们还将证明，通过\cite{dleBMO}中的一个关于 BMO 范数的新结果，可以放松\cite{dlebook,dlebook1}中的谱隙条件。 显示英文摘要

摘要： 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}.