J. Burczak

activity

20122026

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6 papers · 1 filter

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.AP2018

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.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…