Yongkui Zou, Professor, Jilin University

Jialin Hong, Professor

Stochastic Kuramoto-Sivashinsky equation and its Kolmogorov equation with application to weak error estimates

14:00-15:00, August 20(Thursday), N219

The aim of this talk is to investigate high-order regularity estimates of the solution to a stochastic Kuramoto--Sivashinsky equation driven by additive noise and associated Kolmogorov equation. We first establish high-order a priori estimates and exponential integrability of the exact mild solution to stochastic Kuramoto--Sivashinsky equation. Then, we derive a priori estimates for both the first and second order Fr\'echet derivatives of the solution to the Kolmogorov equation, including estimates for these derivatives when composed with fractional powers of the Laplacian operator. Finally, as an application, we study weak error estimates of a spectral Galerkin approximation to stochastic Kuramoto--Sivashinsky equation.