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5 votes
0 answers
412 views

Is it really interesting to prove well-posedness of unsolved SPDE?

Lots of nonlinear SPDE remained open for decades (especially the non-deterministic ones in higher dimensions because of the regularity of the noise) until Hairer's breakthrough (regularity structures),...
2 votes
0 answers
93 views

$\Phi_d^3$ SPDE

One of the first prototypes of a singular stochastic PDE is the $\Phi_d^4$ SPDE $$\partial_t u=\Delta u-u^3+\xi,$$ where $\xi$ is space-time white noise. It is difficult to study because $u$ is ...
10 votes
1 answer
1k views

Is there any reason to use paracontrolled calculus over regularity structures?

Paracontrolled calculus was developed by Gubinelli, Imkeller and Perkowski as a way of treating singular stochastic PDEs such as KPZ, $\Phi_3^4$ or PAM, around the same time regularity structures were ...