一类Burgers-Constantin-Lax-Majda方程的奇异性

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

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.