3 papers
math.AP2026
On the non-uniqueness of solutions of the axi-symmetric swirl-free Navier-Stokes equations, I
Alexandru D. Ionescu, Hao Jia, Stan Palasek
In this paper we construct numerically a new class of unstable self-similar solutions of the incompressible Navier-Stokes equations in . Our solutions are axially sym…
math.AP2025
Quasiperiodic solutions of the generalized SQG equation
Javier Gómez-Serrano, Alexandru D. Ionescu, Jaemin Park
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an e…
math.AP2025
On the wave turbulence theory of 2D gravity waves, I: deterministic energy estimates
Yu Deng, Alexandru D. Ionescu, Fabio Pusateri
Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKE) for water waves models. This problem has received…