S. Palasek

activity

20212025

collaborators

5 papers

math.AP2025

Instantaneous Type I blow-up and non-uniqueness of smooth solutions of the Navier-Stokes equations

Alexey Cheskidov, Mimi Dai, Stan Palasek

For any smooth, divergence-free initial data, we construct a solution of the Navier--Stokes equations that exhibits Type~I blow-up of the $L^{\infty}$ norm at time $T_{*} > 0$ , while rem…

math.AP2025

Arbitrary norm growth in the 3D Navier-Stokes equations

Stan Palasek

We construct a family of smooth initial data for the Navier-Stokes equations, bounded in $B M O^{- 1} (T^{3})$ , that gives rise to arbitrarily large global solutions. As a conseq…

math.AP2025

Non-Uniqueness of Smooth Solutions of the Navier-Stokes Equations from Critical Data

Matei P. Coiculescu, Stan Palasek

We consider the Cauchy problem for the incompressible Navier-Stokes equations in dimension three and construct initial data in the critical space $B M O^{- 1}$ from which there exist…

math.AP2022

Epochs of regularity for wild Hölder-continuous solutions of the Hypodissipative Navier-Stokes System

Aynur Bulut, Manh Khang Huynh, Stan Palasek

We consider the hypodissipative Navier-Stokes equations on $[0, T] \times T^{d}$ and seek to construct non-unique, Hölder-continuous solutions with epochs of regularity (smoo…

math.AP2021

Improved quantitative regularity for the Navier-Stokes equations in a scale of critical spaces

Stan Palasek

We prove a quantitative regularity theorem and blowup criterion for classical solutions of the three-dimensional Navier-Stokes equations satisfying certain critical conditions. The…