## DG-MP-PDE Seminar: Well-posedness of stochastic PDEs

• Date: 02/04/2010
Lecturer(s):
Location:

University of British Columbia

Description:

In this talk, we first discuss the second iteration argument introduced
by Bourgain to establish LWP of KdV with measures as initial data.
Then, we establish LWP of the stochastic KdV (SKdV) with additive
space-time white noise by estimating the stochastic convolution via Ito
calculus and showing its continuity via the factorization method. Next,
we discuss
well-posedness of SKdV with multiplicative noise in $L^2$. In order to
treat the non-zero mean case, we derive a coupled system of a SDE and a
SPDE.

Lastly, as a toy model to study KPZ equation and stochastic Burgers
equation, we study stochastic KdV-Burgers equation (SKdVB). We discuss
how Fourier analytic technique can be applied to show LWP. If time
permits, we discuss how one can obtain global well-posedness of these
equations via (1) analogue of conservation laws, (2) Applying
Bourgain's argument for invariant measures (for deterministic PDEs) to
SPDEs.

Schedule:

3:30pm-4:30pm, WMAX 110