Global well-posedness and inviscid limit for the Korteweg-de Vries-Burgers equation

作者：Guo Zihua^*; Wang Baoxiang

来源：Journal of Differential Equations, 2009, 246(10): 3864-3901.

DOI：10.1016/j.jde.2009.03.006

• KdV-Burgers equation
• Uniform global well-posedness
• Inviscid limit behavior

Considering the Cauchy problem for the Korteweg-de Vries-Burgers equation
u(t) + U(xxx) + epsilon vertical bar partial derivative(x)vertical bar(2 alpha) u + (u(2))(x) = 0, u (0) = phi,
where 0 <= epsilon, alpha <= 1 and u is a real-valued function, we show that it is globally well-posed in H(s) (s > s(alpha)), and uniformly globally well-posed in H(s) (s > -3/4) for all epsilon is an element of (0, 1]. Moreover, we prove that for any T > 0, its solution converges in C([0, T]; H(s)) to that of the KdV equation if epsilon tends to 0.

• 出版日期2009-5-15
• 单位北京大学