In this paper, we study the finite-time singularity formation on the coupled Burgers–Constantin–Lax–Majda system with the nonlocal term, which is one nonlinear nonlocal system of combining Burgers equations with Constantin–Lax–Majda equations. We discuss whether the finite-time blow-up singularity mechanism of the system depends upon the domination between the CLM type’s vortex-stretching term and the Burgers type’s convection term in some sense. We give two kinds of different finite-time blow-up results and prove the local smooth solution of the nonlocal system blows up in finite time for two classes of large initial data.

中文翻译：

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具有非局部项的Burgers-Constantin-Lax-Majda耦合系统的奇异性形成

在本文中，我们研究带有非局部项的Burgers–Constantin–Lax–Majda耦合系统上的有限时间奇异性，这是一个将Burgers方程与Constantin–Lax–Majda方程相结合的非线性非局部系统。在某种意义上，我们讨论系统的有限时间爆炸奇异性机制是否取决于CLM型涡旋拉伸项和Burgers型对流项的支配。我们给出两种不同的有限时间爆炸结果，并证明了对于两类大的初始数据，非局部系统在有限时间内爆炸的局部光滑解。