# Analysis Seminar

#### A New Proof of Landau Damping in the Nonlinear Vlasov Equations

**Speaker:**
Jacob Bedrossian

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, November 14, 2013, 11 a.m.

**Synopsis:**

Landau damping is an important mechanism in kinetic descriptions of plasmas, however, mathematical works on the topic have been relatively scarce. We give a simpler proof of Landau damping in the Vlasov equations on the ND torus, originally due to Mouhot and Villani (2011). Moreover, we may take our initial data in Gevrey class smaller than 3, the regularity requirement conjectured in the original work. The proof combines ideas from the original proof with ideas from our recent work on inviscid damping in 2D Euler (joint with N. Masmoudi). The Newton iteration scheme and Lagrangian estimates of the original work are replaced by paraproduct decompositions and the treatment of the plasma echo resonances is simplified by controlled regularity losses in time. Joint work with N. Masmoudi and C. Mouhot.