Global classical solutions by transport noise for reaction-diffusion systems with entropy dissipation

Abstract: The existence of global classical solutions for reaction-diffusion systems arising from chemical reaction networks remains a major open problem in the deterministic setting, especially for reactions with high polynomial growth. We prove that a suitably chosen, physically motivated transport noise yields unique strong solutions for complex balanced chemical reaction networks that are global in time with arbitrarily high probability. These solutions possess paths in $C^θ_t C<sup>{\infty}_x$ for all $θ&lt;1/2$ and are, in particular, classical in space. Furthermore, we show that a suitable transport noise can enhance the dissipation of spatial fluctuations at an arbitrarily prescribed exponential rate. Our proofs rely on a combination of scaling-limit arguments, maximal $L<sup>p(L<sup>q)$-regularity, and entropy-entropy dissipation estimates.