Analysis of a Singular Boussinesq Model
arXiv:1808.05717
Abstract
Recently, a new singularity formation scenario for the 3D axi-symmetric Euler equation and the 2D inviscid Boussinesq system has been proposed by Hu and Luo based on extensive numerical simulations [15, 16]. As the firrst step to understand the scenario, models with simplified sign-definite Biot-Savart law and forcing have recently been studied in [7, 6, 8, 12, 14, 18]. In this paper, we aim to bring back one of the complications encountered in the original equation - the sign changing kernel in the Biot-Savart law. This makes analysis harder, as there are two competing terms in the fluid velocity integral whose balance determines the regularity properties of the solution. The equation we study here is based on the CKY model introduced in [6]. We prove that finite time blow up persists in a certain range of parameters.
References in corpus (4)
- Potentially Singular Solutions of the 3D Incompressible Euler Equations
- An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations
- Finite time blow up in the hyperbolic Boussinesq system
- Stability of Blow Up for a 1D model of Axisymmetric 3D Euler Equation