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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 of by balls of radius bigger or equal satisfying two conditions: (i) any ball intersects at most 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…