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Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions

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arxiv 2503.08186 v2 pith:HOPE22VU submitted 2025-03-11 math.AP

Hector Bouton , Laurent Desvillettes , Helge Dietert This is my paper · ORCID
classification math.AP
keywords solutionscross-diffusiondimensionsglobalparabolicpartialshigesada-kawasaki-teramotostrong
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abstract

We prove the existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lokta-Volterra reaction terms in three dimensions. A key part is the independent careful study of the parabolic equation $a\partial_t w - \Delta w = f$ with a rough coefficient $a$, homogeneous Neumann boundary conditions, and the special assumption $\partial_tw \ge 0$. By the same method, we obtain estimates for solutions to reaction-diffusion systems modelling reversible chemistry.

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    For complex balanced reaction networks with arbitrarily high polynomial growth, a suitable transport noise yields unique global classical solutions with arbitrarily high probability and enhanced exponential dissipatio...

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