S. Palasek

collaborators

5 papers

math.AP2026

On the non-uniqueness of solutions of the axi-symmetric swirl-free Navier-Stokes equations, I

Alexandru D. Ionescu, Hao Jia, Stan Palasek

In this paper we construct numerically a new class of unstable self-similar solutions of the incompressible Navier-Stokes equations in $R^{3}$ . Our solutions are axially sym…

math.AP2026

Finite-time blow-up in an elementary model of the 3D Navier-Stokes equations

Stan Palasek

We demonstrate finite-time blow-up in a simple, realistic shell model of the 3D Navier-Stokes equations, equipped with "smooth" (i.e., rapidly decaying in frequency) initial data a…

math.AP2026

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…