Blow Up Of A Hyperbolic SQG Model

TL;DR

This paper investigates a modified hyperbolic surface quasi-geostrophic equation, demonstrating finite-time blow-up for a broad range of initial conditions, advancing understanding of singularity formation in fluid dynamics models.

Contribution

It introduces a new hyperbolic SQG model with a modified Biot-Savart law and proves finite-time blow-up for many initial data sets.

Findings

Finite-time blow-up demonstrated for the model

Broad class of initial data leads to singularity

Advances understanding of blow-up mechanisms in SQG models

Abstract

This paper studies of a variation of the hyperbolic blow up scenario suggested by Hou and Luo's recent numerical simulation [12]. In particular, we propose a "hyperbolic" surface quasi-geostrophic equation characterized by a incompressible velocity field with a modified Biot-Savart law. For this model, we will show Finite time blow up for a wide class of initial data.