一类Burgers-Constantin-Lax-Majda方程的奇异性  

The Singularity Formation for Burgers-Constantin-Lax-Majda Equation

作　　者：李林锐[1] 王术[2] 王长有[3] 

机构地区：[1]防灾科技学院基础部,河北三河065201 [2]北京工业大学应用数理学院,北京100124 [3]重庆邮电大学应用数学研究所,重庆400065

出　　处：《重庆师范大学学报（自然科学版）》2016年第2期90-94,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11371042);青年科学基金资助项目(No.201207)

摘　　要：研究了一类广义的Burgers-Constantin-Lax-Majda方程的奇异性问题,这类方程同时具有Burgers方程和Constantin-Lax-Majda方程的许多性质,同时带有非局部项uHu(其中H表示Hilbert变换),证明了这类方程在非负的初始条件下,其解在有限时间内是爆破的,这些结果在很大程度上推广和延伸了先前的相关结果。This paper is concerned with the singularity for a class oF generalized Burgers-Constantin：Lax-Majda equation, which has been proposed as a model which shares many properties of the Burgers equation and Constantin-Lax-Majda equation, meanwhile the model has a nonlocal flux of the form uHu where H is the Hilbert transform. We prove the blow up in finite time for a class of non- negative initial data; the main results improve and extend the ones in the previous works to a large extent.

关 键 词：Burgers-Constantin-Lax-Majda方程 有限时间奇异性 Hilbert变换 非线性非局部系统 

分 类 号：O175.29[理学—数学]