Reaction-diffusion SPDEs with non-trace-class multiplicative noise are shown to be locally well-posed in critical Besov spaces of initial data, with regularization, blow-up criteria, and positivity.
arXiv preprint arXiv:1811.08356 , year=
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An optimal local theory for reaction-diffusion equations driven by non-trace-class noise
Reaction-diffusion SPDEs with non-trace-class multiplicative noise are shown to be locally well-posed in critical Besov spaces of initial data, with regularization, blow-up criteria, and positivity.