摘要
This current paper is devoted to the Cauchy problem for higher order dispersive equation ut＋δx^2n＋1u=δx（uδx^nu）＋δx^n-1（ux^2）, n ≥ 2, n ∈ N^＋. Ut By using Besov-type spaces, we prove that the associated problem is locally well-posed in H（-n/2＋3/4,-1/2n）. The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H^（s,a）（R） with s〈-n/2＋3/4 and all a∈R.
This current paper is devoted to the Cauchy problem for higher order dispersive equation ut＋δx^2n＋1u=δx（uδx^nu）＋δx^n-1（ux^2）, n ≥ 2, n ∈ N^＋. Ut By using Besov-type spaces, we prove that the associated problem is locally well-posed in H（-n/2＋3/4,-1/2n）. The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H^（s,a）（R） with s〈-n/2＋3/4 and all a∈R.
基金
supported by Natural Science Foundation of China NSFC(11401180 and 11471330)
supported by the Young Core Teachers Program of Henan Normal University(15A110033)
supported by the Fundamental Research Funds for the Central Universities(WUT:2017 IVA 075)
