Nonlinear inviscid dam** near monotonic shear flows

AD Ionescu, H Jia - ar** near the Couette flow in a channel
AD Ionescu, H Jia - Communications in Mathematical Physics, 2020‏ - Springer
We prove asymptotic stability of the Couette flow for the 2D Euler equations in the domain T
* 0, 1 T× 0, 1. More precisely we prove that if we start with a small and smooth perturbation …

Long time dynamics of forced critical SQG

P Constantin, A Tarfulea, V Vicol - Communications in Mathematical …, 2015‏ - Springer
We prove the existence of a compact global attractor for the dynamics of the forced critical
surface quasi-geostrophic equation (SQG) and prove that it has finite fractal (box-counting) …

On the local well-posedness of the Prandtl and hydrostatic Euler equations with multiple monotonicity regions

I Kukavica, N Masmoudi, V Vicol, TK Wong - SIAM Journal on Mathematical …, 2014‏ - SIAM
We find a new class of data for which the Prandtl boundary layer equations and the
hydrostatic Euler equations are locally in time well-posed. In the case of the Prandtl …

Mathematics and turbulence: where do we stand?

CW Bardos, ES Titi - Journal of Turbulence, 2013‏ - Taylor & Francis
This contribution covers the topics presented by the authors at the “Fundamental Problems
of Turbulence, 50 Years after the Marseille Conference 1961” meeting that took place in …

[PDF][PDF] On the local existence of analytic solutions to the Prandtl boundary layer equations

I Kukavica, V Vicol - Commun. Math. Sci, 2013‏ - academia.edu
We address the local well-posedness of the Prandtl boundary layer equations. Using a new
change of variables we allow for more general data than previously considered, that is, we …

Time-analyticity of Lagrangian particle trajectories in ideal fluid flow

V Zheligovsky, U Frisch - Journal of Fluid Mechanics, 2014‏ - cambridge.org
It is known that the Eulerian and Lagrangian structures of fluid flow can be drastically
different; for example, ideal fluid flow can have a trivial (static) Eulerian structure, while …

Axi‐symmetrization near point vortex solutions for the 2D Euler equation

A Ionescu, H Jia - Communications on Pure and Applied …, 2022‏ - Wiley Online Library
We prove asymptotic stability of point vortex solutions to the full Euler equation in two
dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported …

Linear vortex symmetrization: the spectral density function

AD Ionescu, H Jia - Archive for Rational Mechanics and Analysis, 2022‏ - Springer
We investigate solutions of the 2 d incompressible Euler equations, linearized around
steady states which are radially decreasing vortices. Our main goal is to understand the …

[HTML][HTML] Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models

P Constantin, V Vicol, J Wu - Advances in Mathematics, 2015‏ - Elsevier
We discuss general incompressible inviscid models, including the Euler equations, the
surface quasi-geostrophic equation, incompressible porous medium equation, and …