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8 papers · 2 filters
Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems
Tarek M. Elgindi, Klaus Widmayer
At the core of this article is an improved, sharp dispersive estimate for the anisotropic linear semigroup arising in both the study of the dispersive SQG equation and…
Enhanced dissipation and inviscid damping in the inviscid limit of the Navier-Stokes equations near the 2D Couette flow
Jacob Bedrossian, Nader Masmoudi, Vlad Vicol
In this work we study the long time, inviscid limit of the 2D Navier-Stokes equations near the periodic Couette flow, and in particular, we confirm at the nonlinear level the quali…
Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
Fanghua Lin, Changyou Wang
The study of hydrodynamics of liquid crystal leads to many fasci- nating mathematical problems, which has prompted various interesting works recently. This article reviews the stat…
The Froude number for solitary water waves with vorticity
Miles H. Wheeler
We consider two-dimensional solitary water waves on a shear flow with an arbitrary distribution of vorticity. Assuming that the horizontal velocity in the fluid never exceeds the w…
Dissipative Euler flows with Onsager-critical spatial regularity
Tristan Buckmaster, Camillo De Lellis, László Székelyhidi
For any we show the existence of continuous periodic weak solutions of the Euler equations which do not conserve the kinetic energy and belong to the space $L^1_t (C_x^{\…
Global Small Solutions to a Complex Fluid Model in 3D
Fanghua Lin, Ting Zhang
In this paper, we provide a much simplified proof of the main result in [Lin and Zhang, Comm. Pure Appl. Math.,67(2014), 531--580] concerning the global existence and uniqueness of…