64 citations · 90 across the 6 of their papers we have counts for
6 papers
On Vorticity Gradient Growth for the Axisymmetric 3D Euler Equations Without Swirl
Tam Do
We consider the 3D axisymmetric Euler equations without swirl on some bounded axial symmetric domains. In this setting, well-posedness is well known due to the essentially 2D geome…
Global regularity for the fractional Euler alignment system
Tam Do, Alexander Kiselev, Lenya Ryzhik +1
We study a pressureless Euler system with a nonlinear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the se…
Stability of Blow Up for a 1D model of Axisymmetric 3D Euler Equation
Tam Do, Alexander Kiselev, Xiaoqian Xu
The question of the global regularity vs finite time blow up in solutions of the 3D incompressible Euler equation is a major open problem of modern applied analysis. In this paper,…
One-dimensional model equations for hyperbolic fluid flow
Tam Do, Vu Hoang, Maria Radosz +1
In this paper we study the singularity formation for two nonlocal 1D active scalar equations, focusing on the hyperbolic flow scenario. Those 1D equations can be regarded as simpli…
A Discrete Model for Nonlocal Transport Equations with Fractional Dissipation
Tam Do
In this note, we propose a discrete model to study one-dimensional transport equations with non-local drift and supercritical dissipation. The inspiration for our model is the equa…
On a 1D transport equation with nonlocal velocity and supercritical dissipation
Tam Do
We study a 1D transport equation with nonlocal velocity. First, we prove eventual regularization of the viscous regularization when dissipation is in the supercritical range with n…