W. Ożański

activity

20162026

most citedLeray's fundamental work on the Navier-Stokes equations: a modern review of "Sur le mouvement d'un liquide visqueux emplissant l'espace"

24 citations · 90 across the 33 of their papers we have counts for

collaborators

35 papers

math.AP2026

An analysis of aerodynamic properties of delta wings

Wojciech Ożański

We consider a sharp-edge delta wing of small aspect ratio $A > 0$ , which is an example of a 3D airfoil whose aerodynamic properties cannot be modeled using the potential lift}only. A…

math.AP2026

Gevrey instability in the inviscid inflow-outflow problem

Igor Kukavica, Wojciech Ożański, 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

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

I. Kukavica, W. S. Ożański

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.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. Ożański

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 $σ > 0$ other balls, and (ii)…

math.AP2025

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

In-Jee Jeong, Luis Martínez-Zoroa, Wojciech S. Ożański

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

math.AP2024

Exact boundary controllability of the 3D incompressible ideal MHD system

Igor Kukavica, Wojciech S. Ożański

We consider the three-dimensional ideal MHD system on a domain $Ω^{'} \subset R^{3}$ with a part $Γ$ of the boundary~ $\partial Ω$ , where we prescribe both $u \cdot n$ and $b\cdo…

math.AP2024★ 1 cited

Instantaneous continuous loss of regularity for the SQG equation

Diego Córdoba, Luis Martínez-Zoroa, Wojciech S. Ożański

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

math.AP2023★ 1 cited

A simple proof of linear instability of shear flows with application to vortex sheets

Anuj Kumar, Wojciech Ożański

We consider the construction of linear instability of parallel shear flows, which was developed by Zhiwu Lin (SIAM J. Math. Anal. 35(2), 2003). We give an alternative simple proof…

math.AP2023

An improvement to Prandtl's 1933 model for minimizing induced drag

Wojciech Ożański

We consider Prandtl's 1933 model for calculating circulation distribution function $Γ$ of a finite wing which minimizes induced drag, under the constraints of prescribed total lift…

math.AP2023

Linear and nonlinear instability of vortex columns

Dallas Albritton, Wojciech Ożański

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

math.AP2023

The inviscid inflow-outflow problem via analyticity

Igor Kukavica, Wojciech Ożański, Marco Sammartino

We consider the incompressible Euler equation on an analytic domain $Ω$ with nonhomogeneous boundary condition $u \cdot n = u \cdot n$ on $\partial Ω$ ,…

math.AP2023

Construction of the free-boundary 3D incompressible Euler flow under limited regularity

Mustafa Sencer Aydin, Igor Kukavica, Wojciech S. Ożański +1

We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We construct unique local-in-time solutions in the Lagrangian setting fo…

math.AP2023

Linear instability of symmetric logarithmic spiral vortex sheets

Tomasz Cieślak, Piotr Kokocki, Wojciech S. Ożański

We consider Alexander spirals with $M \geq 3$ branches, that is symmetric logarithmic spiral vortex sheets. We show that such vortex sheets are linearly unstable in the $L^{\infty}$ (…

math.AP2022

Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations

Diego Córdoba, Luis Martínez-Zoroa, Wojciech Ożański

We construct solutions of the 2D incompressible Euler equations in $\mathds{R}^2\times [0,\infty)$ such that initially the velocity is in the super-critical Sobolev space $H^{β}$ for…

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

On a model of an elastic body fully immersed in a viscous incompressible fluid with small data

Igor Kukavica, Wojciech S. Ożański

We consider a model of an elastic body immersed between two layers of incompressible viscous fluid. The elastic displacement $w$ is governed by the damped wave equation $w_{tt} + α…

math.AP2022★ 1 cited

Existence of nonsymmetric logarithmic spiral vortex sheet solutions to the 2D Euler equations

T. Cieślak, P. Kokocki, W. S. Ożański

We consider solutions of the 2D incompressible Euler equation in the form of $M \geq 1$ cocentric logarithmic spirals. We prove the existence of a generic family of spirals that are…

math.AP2022

Global-in-time stability of ground states of a pressureless hydrodynamic model of collective behaviour

P. B. Mucha, W. S. Ożański

We consider a pressureless hydrodynamic model of collective behaviour, which is concerned with a density function $ρ$ and a velocity field $v$ on the torus, and is described by the…

math.AP2021

Global well-posedness and exponential decay for a fluid-structure model with small data

Igor Kukavica, Wojciech S. Ożański

We address the system of partial differential equations modeling motion of an elastic body interacting with an incompressible fluid. The fluid is modeled by the incompressible Navi…

math.AP2021

Well-posedness of logarithmic spiral vortex sheets

T. Cieślak, P. Kokocki, W. S. Ożański

We consider a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aero-dynamik, 1922)…

math.AP2021★ 2 cited

Quantitative transfer of regularity of the incompressible Navier-Stokes equations from $R^{3}$ to the case of a bounded domain

Wojciech S. Ożański

Let $u_{0} \in C_{0}^{5} (B_{R_{0}})$ be divergence-free and suppose that $u$ is a strong solution of the three-dimensional incompressible Navier-Stokes equations on $[0, T]$ in the whole s…

math.AP2021

Local-in-time existence of free-surface 3D Euler flow with $H^{2 + δ}$ initial vorticity in a neighborhood of the free boundary

Igor Kukavica, Wojciech S. Ożański

We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that $u_{0} \in H^{2.5 + δ}$ is such that $\mathrm{curl}\,u_0 \in…

math.AP2021★ 2 cited

A partial uniqueness result and an asymptotically sharp nonuniqueness result for the Zhikov problem on the torus

Tomasz Cieślak, Wojciech S. Ożański

We consider the stationary diffusion equation $- div (\nabla u + b u) = f$ in $n$ -dimensional torus $T^{n}$ , where $f \in H^{- 1}$ is a given forcing and $b \in L^{p}$ is a…

math.AP2021★ 3 cited

An anisotropic regularity condition for the 3D incompressible Navier-Stokes equations for the entire exponent range

Igor Kukavica, Wojciech S. Ożański

We show that a suitable weak solution to the incompressible Navier-Stokes equations on $R^{3} \times (- 1, 1)$ is regular on $R^{3} \times (0, 1]$ if $\partial_{3} u$ belon…

An analysis of aerodynamic properties of delta wings

Gevrey instability in the inviscid inflow-outflow problem

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

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

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

Exact boundary controllability of the 3D incompressible ideal MHD system

Instantaneous continuous loss of regularity for the SQG equation

A simple proof of linear instability of shear flows with application to vortex sheets

An improvement to Prandtl's 1933 model for minimizing induced drag

Linear and nonlinear instability of vortex columns

The inviscid inflow-outflow problem via analyticity

Construction of the free-boundary 3D incompressible Euler flow under limited regularity

Linear instability of symmetric logarithmic spiral vortex sheets

Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations

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

On a model of an elastic body fully immersed in a viscous incompressible fluid with small data

Existence of nonsymmetric logarithmic spiral vortex sheet solutions to the 2D Euler equations

Global-in-time stability of ground states of a pressureless hydrodynamic model of collective behaviour

Global well-posedness and exponential decay for a fluid-structure model with small data

Well-posedness of logarithmic spiral vortex sheets

Quantitative transfer of regularity of the incompressible Navier-Stokes equations from R3 to the case of a bounded domain

Local-in-time existence of free-surface 3D Euler flow with H2+δ initial vorticity in a neighborhood of the free boundary

A partial uniqueness result and an asymptotically sharp nonuniqueness result for the Zhikov problem on the torus

An anisotropic regularity condition for the 3D incompressible Navier-Stokes equations for the entire exponent range

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

Quantitative transfer of regularity of the incompressible Navier-Stokes equations from $R^{3}$ to the case of a bounded domain

Local-in-time existence of free-surface 3D Euler flow with $H^{2 + δ}$ initial vorticity in a neighborhood of the free boundary