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 dissipation of spatial fluctuations.
Global solutions to quadratic systems of stochastic reaction-diffusion equations in space-dimension two
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abstract
We prove the existence of global-in-time regular solutions to a system of stochastic quadratic reaction-diffusion equations. Global-in-time existence is based on a $L^\infty$-estimate obtained by an approach {\`a} la De Giorgi, as in [GoudonVasseur10]. The adaptation of this technique to the stochastic case requires in its final step an $L^2\ln(L^2)$-bound, furnished by an estimate by duality on the entropy inequality, as in [DesvillettesFellnerPierreVovelle07]. In our stochastic context, and similarly to [DebusscheRoselloVovelle2021], we need to solve a backward SPDE to exploit the duality technique
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Global classical solutions by transport noise for reaction-diffusion systems with entropy dissipation
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 dissipation of spatial fluctuations.