Sub-critical Stochastic Partial Differential Equations

Speaker: Zhenan Wang (University of Washington)

Abstract: We will start with the notion of criticality in stochastic partial differential equations of the following type.

$$u_t=div(A\nabla u)+div F+f+(G_i\cdot\nabla u+g)\dot{w}_t^i$$

We will then introduce regularity results for SPDEs with sub-critical perturbation terms. Among these sub-critical terms, we will specifically talk about properties of the random drift terms, \$G_i\cdot\nabla u\$, and develop techniques to show the regularity property of the solutions. A few problems regarding the critical terms will also be introduced.