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

作者：Guo Zihua^*; Peng Lizhong; Wang Baoxiang; Wang Yuzhao

来源：Advances in Mathematics, 2011, 228(2): 647-677.

DOI：10.1016/j.aim.2011.03.017

• Benjamin-Ono-Burgers equation
• Uniform well-posedness
• Inviscid limit

We prove that the Cauchy problem for the Benjamin-Ono-Burgers equation
partial derivative(t)u - epsilon partial derivative(2)(x)u + H partial derivative(2)(x)u + uu(x) = 0, u(x, 0) = u(0)(x)
is uniformly globally well-posed in H(s) (s >= 1) for all epsilon is an element of [0, 1]. Moreover, we show that as epsilon -> 0 the solution converges to that of Benjamin-Ono equation in C([0, T]: H(s)) (s >= 1) for any T > 0. Our results give an alternative proof for the global well-posedness of the BO equation in H(1)(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 H(1).

• 出版日期2011-10-1
• 单位华北电力大学; 北京大学