# Uniform Well-Posedness and Inviscid Limit for the Benjamin-Ono-Burgers Equation

 SPECIAL MEMBERS SEMINAR Topic: Uniform Well-Posedness and Inviscid Limit for the Benjamin-Ono-Burgers Equation Speaker: Zihua Guo Affiliation: Member, School of Mathematics Date: Monday, December 13 Time/Room: 4:15pm - 5:15pm/S-101

We prove that the Cauchy problem for the Benjamin-Ono-Burgers equation is uniformly globally well-posed in H^1 for all "\epsilon\in [0,1]". Moreover, we show that for any T>0 the solution converges in C([0,T]:H^1) to that of Benjamin-Ono equation as "\epsilon --> 0". Our results give a new proof for the global well-posedness of the BO equation in H^1(R) without using gauge transform, which was first obtained by Tao using gauge transform, and also solve the problem about the inviscid limit behavior in H1.