J. Burczak

activity

20112026

most citedNon Uniqueness of power-law flows

48 citations · 205 across the 25 of their papers we have counts for

collaborators

25 papers

math.AP2026

Scalar anomalous dissipation and optimal regularity via iterated homogenization

Jan Burczak, László Székelyhidi, Bian Wu

For any $β_{0} < 1/3$ we construct divergence free vector fields in $C_{x, t}^{β_{0}}$ and a sequence of diffusivities $κ_{q} ↘ 0$ such that, for an arbitrary initial datum from a l…

math.AP2025

Pathological solutions of Navier-Stokes equations on $T^{2}$ with gradients in Hardy spaces

Jan Burczak, Antonio Hidalgo-Torné

For an arbitrary smooth initial datum, we construct multiple nonzero solutions to the $2$ d Navier-Stokes equations, with their gradients in the Hardy space $H^{p}$ with any…

math.AP2023★ 2 cited

Anomalous dissipation and Euler flows

Jan Burczak, László Székelyhidi, Bian Wu

We show anomalous dissipation of scalars advected by weak solutions to the incompressible Euler equations with $C^{(\sfrac{1}{3})^-}$ regularity, for an arbitrary initial datum in…

math.AP2022★ 1 cited

Anomalous energy flux in critical $L^{p}$ -based spaces

Jan Burczak, Gabriel Sattig

We construct a three-dimensional vector field that exhibits positive energy flux at every Littlewood-Paley shell and has the best possible regularity in $L^{p}$ -based spaces, $p \le…

math.AP2020★ 48 cited

Non Uniqueness of power-law flows

Jan Burczak, Stefano Modena, László Székelyhidi

We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension $d \geq 2$ . For the power index $q$ below the compactne…

math.AP2020★ 5 cited

On regularity properties of a surface growth model

Jan Burczak, Wojciech S. Ożański, Gregory Seregin

We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally ou…

math.AP2018★ 9 cited

Well posedness of nonlinear parabolic systems beyond duality

Miroslav Bulicek, Jan Burczak, Sebastian Schwarzacher

We develop a methodology for proving well-posedness in optimal regularity spaces for a wide class of nonlinear parabolic initial-boundary value systems, where the standard monotone…

math.AP2017

Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations

Jan Burczak, Rafael Granero-Belinchón

In this paper we consider a $d$ -dimensional ( $d = 1, 2$ ) parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order $α \in (0, 2)$ . We prove un…

math.AP2017

$L l o g L$ -integrability of the velocity gradient for Stokes system with drifts in $L_{\infty} (B M O^{- 1})$

Jan Burczak, Gregory Seregin

For any weak solution of the Stokes system with drifts in $L_{\infty} (B M O^{- 1})$ , we prove a reverse Hölder inequality and $L l o g L$ -higher integrability of the velocity gradients.

math.AP2017★ 3 cited

Stress-diffusive regularizations of non-dissipative rate-type materials

Jan Burczak, Josef Málek, Piotr Minakowski

We consider non-dissipative (elastic) rate-type material models that are derived within the Gibbs-potential-based thermodynamic framework. Since the absence of any dissipative mech…

math.AP2016

Existence and smoothness for a class of $n$ D models in elasticity theory of small deformations

Miroslav Bulíček, Jan Burczak

We consider a model for deformations of a homogeneous isotropic body, whose shear modulus remains constant, but its bulk modulus can be a highly nonlinear function. We show that fo…

math.AP2016★ 1 cited

Suppression of blow up by a logistic source in $2$ D Keller-Segel system with fractional dissipation

Jan Burczak, Rafael Granero-Belinchón

We consider a two dimensional parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order $α$ . We obtain existence of global in time regula…

math.AP2016★ 21 cited

A unified theory for some non Newtonian fluids under singular forcing

Miroslav Bulíček, Jan Burczak, Sebastian Schwarzacher

We consider a model of steady, incompressible non-Newtonian flow with neglected convective term under external forcing. Our structural assumptions allow for certain non-degenerate…

math.AP2015★ 2 cited

On the generalized Buckley-Leverett equation

Jan Burczak, Rafael Granero-Belinchón, Garving K. Luli

In this paper we study the generalized Buckley-Leverett equation with nonlocal regularizing terms. One of these regularizing terms is diffusive, while the other one is conservative…

math.AP2015★ 7 cited

Evolutionary, symmetric p-Laplacian. Interior regularity of time derivatives and its consequences

Jan Burczak, Petr Kaplický

We consider the evolutionary symmetric $p$ -Laplacian with safety $1$ . By symmetric we mean that the full gradient of $p$ -Laplacian is replaced by its symmetric part, which causes b…

math.AP2015

Interior regularity of space derivatives to an evolutionary, symmetric $φ$ -Laplacian

Jan Burczak, Petr Kaplický

We consider Orlicz-growth generalization to evolutionary $p$ -Laplacian and to the evolutionary symmetric $p$ -Laplacian. We derive the spatial second-order Caccioppoli estimate for…

math.AP2015★ 33 cited

Global solutions for a supercritical drift-diffusion equation

Jan Burczak, Rafael Granero-Belinchón

We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation…

math.AP2015★ 27 cited

Critical Keller-Segel meets Burgers on $S^{1}$ : large-time smooth solutions

Jan Burczak, Rafael Granero-Belinchón

We show that solutions to the parabolic-elliptic Keller-Segel system on $S^{1}$ with critical fractional diffusion $(- Δ)^{\frac{1}{2}}$ remain smooth for any initial data and…

math.AP2014

Boundedness of large-time solutions to a chemotaxis model with nonlocal and semilinear flux

Jan Burczak, Rafael Granero-Belinchón

A semilinear version of parabolic-elliptic Keller-Segel system with the \emph{critical} nonlocal diffusion is considered in one space dimension. We show boundedness of weak solutio…

math.AP2014★ 2 cited

Quantitative robustness of regularity for 3D Navier-Stokes system in $H ˙^{α}$ -spaces

Jan Burczak, Wojciech M. Zajączkowski

We present stability and regularity results for the $3$ D incompressible Navier-Stokes system in a periodic box, in $H ˙^{α}$ spaces, with $α \in [1/2, 1]$ . A special attent…

math.AP2014★ 43 cited

On a generalized doubly parabolic Keller-Segel system in one spatial dimension

Jan Burczak, Rafael Granero-Belinchón

We study a doubly parabolic Keller-Segel system in one spatial dimension, with diffusions given by fractional laplacians. We obtain several local and global well-posedness results…

math.AP2012

Boundary De Giorgi-Ladyzhenskaya classes and their application to regularity of swirl of Navier-Stokes

Jan Burczak

The embeddings theorem of space-boundary-type DeGiorgi-Ladyzhenskaya parabolic classes into Holder spaces is presented, which is useful for regularity considerations for parabolic…

math.AP2012

Almost everywhere Hölder continuity of gradients to non-diagonal parabolic systems

Jan Burczak

We present a local almost everywhere regularity result for a general nonlinear non-diagonal parabolic system, which main part depends on symmetric part of the gradient.

math.AP2012

L^{\infty} a priori bounds for gradients of solutions to quasilinear inhomogenous fast-growing parabolic systems

Jan Burczak

We prove boundedness of gradients of solutions to quasilinear parabolic system, the main part of which is a generalization to p-Laplacian and its right hand side's growth depending…

Scalar anomalous dissipation and optimal regularity via iterated homogenization

Pathological solutions of Navier-Stokes equations on T2 with gradients in Hardy spaces

Anomalous dissipation and Euler flows

Anomalous energy flux in critical Lp-based spaces

Non Uniqueness of power-law flows

On regularity properties of a surface growth model

Well posedness of nonlinear parabolic systems beyond duality

Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations

LlogL-integrability of the velocity gradient for Stokes system with drifts in L∞​(BMO−1)

Stress-diffusive regularizations of non-dissipative rate-type materials

Existence and smoothness for a class of nD models in elasticity theory of small deformations

Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation

A unified theory for some non Newtonian fluids under singular forcing

On the generalized Buckley-Leverett equation

Evolutionary, symmetric p-Laplacian. Interior regularity of time derivatives and its consequences

Interior regularity of space derivatives to an evolutionary, symmetric φ-Laplacian

Global solutions for a supercritical drift-diffusion equation

Critical Keller-Segel meets Burgers on S1: large-time smooth solutions

Boundedness of large-time solutions to a chemotaxis model with nonlocal and semilinear flux

Quantitative robustness of regularity for 3D Navier-Stokes system in H˙α-spaces

On a generalized doubly parabolic Keller-Segel system in one spatial dimension

Boundary De Giorgi-Ladyzhenskaya classes and their application to regularity of swirl of Navier-Stokes

Almost everywhere Hölder continuity of gradients to non-diagonal parabolic systems

L^{\infty} a priori bounds for gradients of solutions to quasilinear inhomogenous fast-growing parabolic systems

Pathological solutions of Navier-Stokes equations on $T^{2}$ with gradients in Hardy spaces

Anomalous energy flux in critical $L^{p}$ -based spaces

$L l o g L$ -integrability of the velocity gradient for Stokes system with drifts in $L_{\infty} (B M O^{- 1})$

Existence and smoothness for a class of $n$ D models in elasticity theory of small deformations

Suppression of blow up by a logistic source in $2$ D Keller-Segel system with fractional dissipation

Interior regularity of space derivatives to an evolutionary, symmetric $φ$ -Laplacian

Critical Keller-Segel meets Burgers on $S^{1}$ : large-time smooth solutions

Quantitative robustness of regularity for 3D Navier-Stokes system in $H ˙^{α}$ -spaces