Thomas Y. Hou

collaborators

7 papers

math.AP2026

Nonuniqueness of the $2$ D Euler Evolutions with $L^{1} \cap L^{p}$ Vorticity

Thomas Y. Hou, Xiang Qin, Peicong Song +1

For each prescribed $1 < p < \infty$ , we construct a compactly supported initial vorticity in $L^{1} (R^{2}) \cap L^{p} (R^{2})$ that admits two distinct evolutions under the un…

math.AP2026

A Sharp Uniqueness-Nonuniqueness Dichotomy for Neutral Vortex Arrays in $2$ D Euler Equations

Thomas Y. Hou, Xiang Qin, Peicong Song +1

We establish a sharp uniqueness--nonuniqueness criterion for the two-dimensional incompressible Euler equations within a class of stationary arrays of disjoint neutral vortices. Le…

math.AP2026

On the Stability of Type II Blowup for the Keller-Segel System in High Dimensions

Thomas Y. Hou, Xiang Qin, Peicong Song +1

We study finite-time blowup for the parabolic--elliptic Keller--Segel system on $R^{d}$ in dimensions $d \geq 11$ , where the problem is mass supercritical. For every integer $…

math.AP2026

Exact Blowup Analysis for the Weak-Advection Hou--Li Model

Thomas Y. Hou, Xiang Qin, Xiuyuan Wang

We study self-similar singularity formation for the one-dimensional weak-advection Hou--Li model, a reduced model motivated by the axisymmetric Euler equations. In the periodic set…

math.AP2026

Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy

Thomas Y. Hou, Xiang Qin, Yannick Sire +1

We study the singularity formation mechanisms of the inviscid generalized Surface Quasi-Geostrophic (gSQG) equation on the whole space $R^{2}$ and on the upper half-plane $\…

math.AP2026

Forward Self-Similar Solutions to the 2D Hypodissipative Navier-Stokes Equations

Thomas Y. Hou, Peicong Song

We study the forward self-similar solutions to the $2$ D hypodissipative Navier-Stokes equation with fractional diffusion $(- Δ)^{α}$ for $\frac{1}{2} < α < 1$ . We first show that for arbi…

math.AP2024

Nearly self-similar blowup of generalized axisymmetric Navier-Stokes equations

Thomas Y. Hou

We numerically investigate the nearly self-similar blowup of the generalized axisymmetric Navier--Stokes equations. First, we rigorously derive the axisymmetric Navier--Stokes equa…

Nonuniqueness of the 2D Euler Evolutions with L1∩Lp Vorticity

A Sharp Uniqueness-Nonuniqueness Dichotomy for Neutral Vortex Arrays in 2D Euler Equations

On the Stability of Type II Blowup for the Keller-Segel System in High Dimensions

Exact Blowup Analysis for the Weak-Advection Hou--Li Model

Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy

Forward Self-Similar Solutions to the 2D Hypodissipative Navier-Stokes Equations

Nearly self-similar blowup of generalized axisymmetric Navier-Stokes equations

Nonuniqueness of the $2$ D Euler Evolutions with $L^{1} \cap L^{p}$ Vorticity

A Sharp Uniqueness-Nonuniqueness Dichotomy for Neutral Vortex Arrays in $2$ D Euler Equations