We shall present an (implicit) representation theorem of solutions to a class of linear parabolic equations in terms of the laws of Brownian fluid particles (diffusions with fluid velocity) in a forward manner, obtained by using the duality of fundamental solutions. We then explain how we apply the representation theorem, together with a key idea from the Large Eddy Simulations, to numerically solve viscous fluid flow equations (Navier-Stokes equations) near the boundary.
The talk is based on several recent work with Jian-Guo Liu, Zhihao Guo and Vladislav Cherepanov
