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Nonlinear inviscid dam** near monotonic shear flows
AD Ionescu, H Jia - ar** near the Couette flow in a channel
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 …
* 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
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) …
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
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 …
hydrostatic Euler equations are locally in time well-posed. In the case of the Prandtl …
Mathematics and turbulence: where do we stand?
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 …
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
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 …
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
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 …
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
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 …
dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported …
Linear vortex symmetrization: the spectral density function
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 …
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
We discuss general incompressible inviscid models, including the Euler equations, the
surface quasi-geostrophic equation, incompressible porous medium equation, and …
surface quasi-geostrophic equation, incompressible porous medium equation, and …