I. Kukavica

activity

20232026

collaborators

13 papers

math.AP2026

Persistence of conormal analyticity for the Euler equations in the half-space

Benjamin Ingimarson, Igor Kukavica, Marco Sammartino

We prove the persistence of conormal analyticity through the $H^{r}$ norm, with $r \geq 4$ , for the 3D incompressible Euler equations in the half-space $Ω = R_{+}^{3}$ . We also e…

math.AP2026

Quantitative Parabolic Decay With Bounded Drift

Igor Kukavica, Qi Xu

A bounded time-dependent drift together with an arbitrarily small real potential can produce double exponential decay of the full spatial $L^{2}$ norm. We prove matching quantitative…

math.AP2026

Quantitative Decay for Linear Parabolic Equations

Igor Kukavica, Qi Xu

We establish sharp temporal lower bounds for the full spatial $L^{2}$ -norm of energy solutions to $\partial_{t} u - Δ u = v u$ on $R^{n}$ , with $n \geq 3$ . For global solutions, nonvanis…

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.AP2026

Euler Immersion

Igor Kukavica, Amjad Tuffaha, Qi Xu

We address the Euler immersion problem, a fluid-structure interaction problem in which an elastic body is immersed in an incompressible inviscid fluid governed by the Euler equatio…

math.AP2026

On the blowup rate of vorticity for the Euler equations in a bounded domain

Benjamin Ingimarson, Igor Kukavica

Given that a solution to the 3D incompressible Euler equations on a bounded domain blows up at a time $T_{*}$ and that $T_{*}$ is the first such time, we provide pointwise-in-tim…

math.AP2026

Lower bounds on the blowup rate of vorticity in the Euler equations

Benjamin Ingimarson, Igor Kukavica

Under the assumption that a solution to the 3D incompressible Euler equations blows up at a time $T_{*}$ and that $T_{*}$ is the first such time, we establish lower bounds on th…

math.AP2026

Stabilization of an incompressible fluid-elastic structure system using a vacuum bubble

B. Ingimarson, I. Kukavica, W. S. Ożański

We prove a priori estimates for the system of partial differential equations modeling the interaction between an elastic body and an incompressible fluid in a 3D curved domain. The…

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

On the local analyticity for the Euler equations

Igor Kukavica, Maria Carmela Lombardo, Marco Sammartino

In this paper, we study the existence and uniqueness of solutions to the Euler equations with initial conditions that exhibit analytic regularity near the boundary and Sobolev regu…

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.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 $\partial Ω$ ,…