Wen-Han Zhang

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math.AP2026

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 $R^{3}$ and a continuum of pairwise distinct suitable Leray--Hopf solutions of the unforced three-dimensional Navi…

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…

A Viscous Cascade Construction of Nonunique Leray--Hopf Solutions to the Unforced 3D Navier--Stokes Equations

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

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