J. Burczak

collaborators

3 papers

math.AP2026

Scalar anomalous dissipation and optimal regularity via iterated homogenization

Jan Burczak, LÃ¡szlÃ³ SzÃ©kelyhidi, Bian Wu

For any $I^_{0}^{2} < 1/3$ we construct divergence free vector fields in $C_{x, t}^{I^_{0}^{2}}$ and a sequence of diffusivities $I^º_{q} ↘ 0$ such that, for an arbitrary initial datum from…

math.AP2025

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

Jan Burczak, Antonio Hidalgo-TornÃ©

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.AP2024

Anomalous dissipation and Euler flows

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…

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

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