TY - JOUR

T1 - Uniform well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

AU - Guo, Zihua

AU - Peng, Lizhong

AU - Wang, Baoxiang

AU - Wang, Yuzhao

PY - 2011

Y1 - 2011

N2 - We prove that the Cauchy problem for the Benjamin-Ono-Burgers equation is uniformly globally well-posed in Hs (s? 1) for all ??[0,1]. Moreover, we show that as ??0 the solution converges to that of Benjamin-Ono equation in C([0,T]:Hs) (s?1) for any T>0. Our results give an alternative proof for the global well-posedness of the BO equation in H1(R) without using gauge transform, which was first obtained by Tao (2004) [23], and also solve the problem addressed in Tao (2004) [23] about the inviscid limit behavior in H1.

AB - We prove that the Cauchy problem for the Benjamin-Ono-Burgers equation is uniformly globally well-posed in Hs (s? 1) for all ??[0,1]. Moreover, we show that as ??0 the solution converges to that of Benjamin-Ono equation in C([0,T]:Hs) (s?1) for any T>0. Our results give an alternative proof for the global well-posedness of the BO equation in H1(R) without using gauge transform, which was first obtained by Tao (2004) [23], and also solve the problem addressed in Tao (2004) [23] about the inviscid limit behavior in H1.

UR - http://www.sciencedirect.com/science/article/pii/S0001870811001022/pdf?md5=543a82db8bfef6182bd6b9467cc22c09&pid=1-s2.0-S0001870811001022-main.pdf

U2 - 10.1016/j.aim.2011.03.017

DO - 10.1016/j.aim.2011.03.017

M3 - Article

VL - 228

SP - 647

EP - 677

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -