6 papers · 1 filter
A Viscous Cascade Construction of Nonunique Leray--Hopf Solutions to the Unforced 3D Navier--Stokes Equations
Thomas Y. Hou, Xiang Qin, Peicong Song +1
We construct a nonzero divergence-free initial velocity on and a continuum of pairwise distinct suitable Leray--Hopf solutions of the unforced three-dimensional Navi…
Nonuniqueness of the D Euler Evolutions with Vorticity
Thomas Y. Hou, Xiang Qin, Peicong Song +1
For each prescribed , we construct a compactly supported initial vorticity in that admits two distinct evolutions under the un…
A Sharp Uniqueness-Nonuniqueness Dichotomy for Neutral Vortex Arrays in 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…
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 in dimensions , where the problem is mass supercritical. For every integer $…
On the stability of Lamb-Chaplygin dipole for the 2D Euler equation
Zexing Li, Peicong Song, Tao Zhou
The Lamb-Chaplygin dipole is a traveling wave solution to the 2D incompressible Euler equation, whose orbital stability was established in [Abe-Choi, 2022] and [Abe-Choi-Jeong, 202…
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 D hypodissipative Navier-Stokes equation with fractional diffusion for . We first show that for arbi…