Well-posedness of the Cauchy problem of Ostrovsky equation in anisotropic Sobolev spaces |
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Authors: | Hua Wang Shangbin Cui |
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Institution: | Department of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, People's Republic of China |
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Abstract: | We study the Cauchy problem of the Ostrovsky equation , with βγ<0. By establishing a bilinear estimate on the anisotropic Bourgain space Xs,ω,b, we prove that the Cauchy problem of this equation is locally well-posed in the anisotropic Sobolev space H(s,ω)(R) for any and some . 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,ω)(R) for s?0. |
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Keywords: | Ostrovsky equation Cauchy problem Well-posedness Bilinear estimate Anisotropic Sobolev space |
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