报告人：闫威（河南师范大学）

邀请人：杨美华

报告时间：2022年4月14日 （星期四）10: 00-12:00  

报告地点：腾讯会议：682 6490 4915

报告题目：Convergence problem for the two-dimensional generalized Zakharov-Kuznetsov equation with rough data (I)

报告摘要：In this topic, we consider the we consider the Cauchy problem for the generalized Zakharov-Kuznetsov equation with rough data. Firstly, by using the Fourier restriction norm method, we prove that the Cauchy problem for the generalized Zakharov-Kuznetsov equation is locally well-posed in H^s(k = 2; s >1/2; s > 1-2/k,k \geq 3), which simplifies the proof of Kinoshita (Well-posedness for the Cauchy problem of the modified Zakharov-Kuznetsov equation, arXiv:1911.13265.) and present a new proof of Ribaud and Vento(A note on the Cauchy problem for the 2D generalized Zakharov-Kuznetsov equations, C. R. Math. Acad. Sci. Paris, 350(2012), 499-503.). Secondly, following the idea of Compaan (A smoothing estimate for the nonlinear Schrodinger equation, UIUC Research Experience for Graduate Students report, 2013.), we established the uniform convergence of the problem with data in H^s(k = 2; s > 1/2; s > 1-2/(1+k),k\geq 3) with the aid of some trilinear estimates and multilinear estimates established in this paper. Thirdly, we established the pointwise convergence of the problem of the linear Zakharov-Kuznetsov equation with data in \hat{H}^{\frac{4s}{p},\frac{p}{2}}(4\leq p<\infty) with s\geq 1/2,Finally, following the idea ofCompaan, Luc a and G. Sta lani (Pointwise convergence of the Schrodinger flow Int.Math. Res. Not. 1(2021), 596-647.), we present a new proof of lim_{t\rightarrow 0} u(x; t) = u(x; 0) for a.e. (x; y) \in R^2 with data in H^s(R^2)(s > max{1/2,1-2/k}).

报告人简介：闫威，河南师范大学教授，博士生导师，已在国内外重要期刊Ann. Inst. H. Poincaré Anal. Non Linéaire，  Advances in Differential Equations, Differential and integral Equations,  Journal of  Differential Equations等发表多篇文章。研究方向是偏微分方程，调和分析，随机偏微分方程与初值随机化等。