Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222019 | Nonlinear Analysis: Real World Applications | 2018 | 25 Pages |
Abstract
In this paper, we consider the Cauchy problem for the quadratic and cubic Ostrovsky equation with negative dispersion âxutâβâx3u+1kâx(uk)âγu=0,β<0,γ>0,(k=2,3).Firstly, by using the Strichartz estimates instead of the Cauchy-Schwarz inequalities, we give an alternative proof of Lemma 1.2 of Isaza and MejÃa (2006). Secondly, by using the Strichartz estimates instead of the Cauchy-Schwarz inequalities, we give an alternative proof of Lemma 1.3 of Isaza and MejÃa (2007). Thirdly, we prove that the Cauchy problem for the cubic Ostrovsky equation is locally well-posed in Hs(R) with sâ¥14. Finally, we prove that the Cauchy problem for the cubic Ostrovsky equation is not well-posed in Hs(R) with s<14.
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Authors
JunFang Wang, Wei Yan,