Well-posedness of the Cauchy problem of Ostrovsky equation in anisotropic Sobolev spaces

作者：Wang, Hua^*; Cui, Shangbin

来源：Journal of Mathematical Analysis and Applications, 2007, 327(1): 88-100.

DOI：10.1016/j.jmaa.2006.03.091

• Ostrovsky equation
• Cauchy problem
• well-posedness
• bilinear estimate
• anisotropic Sobolev space

We study the Cauchy problem of the Ostrovsky equation partial derivative(t)u - beta partial derivative(3)(x)u - gamma partial derivative(-1)(x)u u partial derivative(x)u = 0, with beta gamma < 0. By establishing a bilinear estimate on the anisotropic Bourgain space X-s.w.b, we prove that the Cauchy problem of this equation is locally well-posed in the anisotropic Sobolev space H-(s,H-w)(R) for any s > -5/8 and some omega is an element of (0, 1/2). Using this result and conservation laws of this equation, we also prove that the Cauchy problem of this equation is globally well-posed in H-(s,H-w)(R) for s > 0.

• 出版日期2007-3-1
• 单位中山大学