**Nathan Pennington**

**Afilliation:**Kansas State Math department

**Title:**Local and Global solutions to the Lagrangian Averaged Navier-Stokes equation with weak initial data

**Abstract:**The Lagrangian Averaged Navier-Stokes equations are a recently derived approximation to the Navier-Stokes equations. As the name suggests, the Lagrangian Averaged Navier-Stokes are derived by averaging at the Lagrangian level, and the resulting PDE has more easily controlled long time behavior than the Navier-Stokes equations. In this talk, we use a non-standard method to prove the existence of global solutions to the equation with initial data $u_0$ in the Besov space $B^{n/p,p}(\mathbb{R}^n)$ for any $2\leq p<\infty$.

**Slides:**PenningtonNathan.pdf