S. Palasek

activity

20132026

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

17 citations · 39 across the 18 of their papers we have counts for

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15 papers · 1 filter

math.AP2026

A logarithmic regularity criterion for the axisymmetric Navier-Stokes equations

Stan Palasek

For axisymmetric solutions of the Navier-Stokes equations in $R^{3}$ , the circulation $Γ = r u^{θ}$ obeys a maximum principle, and the resulting a priori bound on $Γ$ is scale-inv…

math.AP2026

Finite-time blow-up for the real-valued defocusing energy-supercritical NLW

Matthieu Cadiot, Alexandru D. Ionescu, Stan Palasek

We construct real-valued solutions of the defocusing energy-supercritical nonlinear wave equation $\partial_{t}^{2} u - Δ u + u^{p} = 0$ that blow up in finite time from smooth, compactly suppor…

math.AP2026

Cascade mechanisms for Navier-Stokes blow-up

Alexey Cheskidov, Mimi Dai, Stan Palasek

In a recent preprint (arXiv:2511.09556), we exhibited an inverse energy cascade for the 3D Navier-Stokes equations which results in "instantaneous" Type I blow-up and failure of un…

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.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★ 3 cited

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.AP2024

Non-uniqueness in the Leray-Hopf class for a dyadic Navier-Stokes model

Stan Palasek

The uniqueness of Leray-Hopf solutions to the incompressible Navier-Stokes equations remains a significant open question in fluid mechanics. This paper proposes a potential mechani…

math.AP2023★ 3 cited

Non-uniqueness up to the Onsager threshold for the forced SQG equation

Aynur Bulut, Manh Khang Huynh, Stan Palasek

We establish new non-uniqueness results for the forced inviscid surface quasi-geostrophic equation, via an alternating formulation of convex integration techniques. Our results imp…

math.AP2023

Convex integration above the Onsager exponent for the forced Euler equations

Aynur Bulut, Manh Khang Huynh, Stan Palasek

We establish new non-uniqueness results for the Euler equations with external force on $T^{d}$ $(d \geq 3)$ . By introducing a novel alternating convex integration scheme, we…

math.AP2022★ 2 cited

Quantitative control of solutions to the axisymmetric Navier-Stokes equations in terms of the weak $L^{3}$ norm

W. S. Ożański, S. Palasek

We are concerned with strong axisymmetric solutions to the $3$ D incompressible Navier-Stokes equations. We show that if the weak $L^{3}$ norm of a strong solution $u$ on the time int…

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★ 11 cited

A minimum critical blowup rate for the high-dimensional Navier-Stokes equations

Stan Palasek

We prove quantitative regularity and blowup theorems for the incompressible Navier-Stokes equations in $R^{d}$ , $d \geq 4$ when the solution lies in the critical space $L_t^\in…

math.AP2021★ 17 cited

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…

A logarithmic regularity criterion for the axisymmetric Navier-Stokes equations

Finite-time blow-up for the real-valued defocusing energy-supercritical NLW

Cascade mechanisms for Navier-Stokes blow-up

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

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

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

Arbitrary norm growth in the 3D Navier-Stokes equations

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

Non-uniqueness in the Leray-Hopf class for a dyadic Navier-Stokes model

Non-uniqueness up to the Onsager threshold for the forced SQG equation

Convex integration above the Onsager exponent for the forced Euler equations

Quantitative control of solutions to the axisymmetric Navier-Stokes equations in terms of the weak L3 norm

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

A minimum critical blowup rate for the high-dimensional Navier-Stokes equations

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

Quantitative control of solutions to the axisymmetric Navier-Stokes equations in terms of the weak $L^{3}$ norm