W. Ożański

collaborators

9 papers

math.AP2026

The analytic method of constructing local-in-time solutions of the incompressible Euler equations in Sobolev spaces

I. Kukavica, W. S. OÅ¼aÅski

We introduce a new method for constructing local-in-time solutions of the incompressible Euler equations in Sobolev spaces on an arbitrary Sobolev bounded domain. The method is bas…

math.AP2026

Gevrey instability in the inviscid inflow-outflow problem

Igor Kukavica, Wojciech OÅ¼aÅski, Qi Xu

We consider the 2D incompressible Euler equations on a periodic channel $T \times (0, 1)$ with inflow-outflow boundary condition $u = (0, 1)$ on $T \times {0, 1}$ . W…

math.AP2025

Linear and nonlinear instability of vortex columns

Dallas Albritton, Wojciech OÅ¼aÅski

We consider vortex column solutions $v = V (r) e_{I^} ¸ + W (r) e_{z}$ to the $3$ D Euler equations. We give a mathematically rigorous construction of the countable family of unstable modes…

math.AP2025

A unified theory of existence of suitable weak solutions to the 3D incompressible Navier-Stokes equations for non-decaying initial data

A. Balakrishna, I. Kukavica, W. S. OÅ¼aÅski

We consider any cover $C$ of $R^{3}$ by balls of radius bigger or equal $1$ satisfying two conditions: (i) any ball intersects at most $I ¨ > 0$ other balls, and (ii)…

math.AP2025

Instantaneous continuous loss of regularity for the SQG equation

Diego CÃ³rdoba, Luis MartÃnez-Zoroa, Wojciech S. OÅ¼aÅski

Given $s \in (3/2, 2)$ and $ε > 0$ , we construct a compactly supported initial data $I^¸_{0}$ such that $∥ I^¸_{0} ∥_{H^{s}} \leq ε$ and there exist $T > 0$ , $c > 0$ and a lo…

math.AP2025

Instantaneous continuous loss of Sobolev regularity for the 3D incompressible Euler equation

In-Jee Jeong, Luis MartÃnez-Zoroa, Wojciech S. OÅ¼aÅski

We prove instantaneous and continuous-in-time loss of supercritical Sobolev regularity for the 3D incompressible Euler equations in $R^{3}$ . Namely, for any $s \in (0, 3/2)$ …