Finite-time blowup for the inviscid vortex stretching equation
Evan Miller
TL;DR
This paper introduces the inviscid vortex stretching equation as a simplified model for 3D Euler, demonstrating finite-time blowup of smooth solutions and highlighting the importance of advection in preventing singularities.
Contribution
It presents the inviscid vortex stretching equation and proves finite-time blowup of smooth solutions, emphasizing advection's role in vortex dynamics.
Findings
Smooth solutions blow up in finite time
Advection depletes nonlinear vortex stretching
Supports the significance of advection in 3D Euler
Abstract
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.
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Taxonomy
TopicsNavier-Stokes equation solutions · Computational Fluid Dynamics and Aerodynamics · Fluid Dynamics and Turbulent Flows