Finite-time blowup for the inviscid vortex stretching equation
Finite-time blowup for the inviscid vortex stretching equation
复制标题
无粘涡拉伸方程的有限时间膨胀
作者：
E. Miller
本文将引入无粘涡旋拉伸方程，它是忽略涡旋平流的三维欧拉方程的一个模型方程。我们将证明这个方程的光滑解在有限时间内爆破，即使限制在轴对称的无旋流解下也是如此。这进一步证明了平流在消除三维欧拉方程解的非线性涡旋拉伸中的作用。
In this paper, we will introduce the inviscid vortex stretching equation, which is a model equation for the 3D Euler equation where the advection of vorticity is neglected. We will show that there are smooth solutions of this equation which blowup in finite-time, even when restricting to axisymmetric, swirl-free solutions. This provides further evidence of the role of advection in depleting nonlinear vortex stretching for solutions of the 3D Euler equation.