[图书][B] Topological methods in hydrodynamics
VI Arnold, VI Arnold - 2014 - Springer
A group theoretical approach to hydrodynamics considers hydrodynamics to be the
differential geometry of diffeomorphism groups. The principle of least action implies that the …
differential geometry of diffeomorphism groups. The principle of least action implies that the …
Convex integration and phenomenologies in turbulence
T Buckmaster, V Vicol - EMS Surveys in Mathematical Sciences, 2020 - ems.press
In this review article we discuss a number of recent results concerning wild weak solutions of
the incompressible Euler and Navier–Stokes equations. These results build on the …
the incompressible Euler and Navier–Stokes equations. These results build on the …
Singularity formation in the incompressible Euler equation in finite and infinite time
TD Drivas, TM Elgindi - EMS Surveys in Mathematical Sciences, 2023 - ems.press
Some classical and recent results on the Euler equations governing perfect (incompressible
and inviscid) fluid motion are collected and reviewed, with some small novelties scattered …
and inviscid) fluid motion are collected and reviewed, with some small novelties scattered …
Finite-time singularity formation for solutions to the incompressible Euler equations on
TM Elgindi - Annals of Mathematics, 2021 - projecteuclid.org
It has been known since work of Lichtenstein and Gunther in the 1920s that the 3D
incompressible Euler equation is locally well-posed in the class of velocity fields with Hölder …
incompressible Euler equation is locally well-posed in the class of velocity fields with Hölder …
Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data I: Analysis
J Chen, TY Hou - arXiv preprint arXiv:2210.07191, 2022 - arxiv.org
Inspired by the numerical evidence of a potential 3D Euler singularity\cite
{luo2014potentially, luo2013potentially-2}, we prove finite time blowup of the 2D Boussinesq …
{luo2014potentially, luo2013potentially-2}, we prove finite time blowup of the 2D Boussinesq …
[图书][B] Topological methods in hydrodynamics
VI Arnolʹd, BA Khesin - 2009 - Springer
Preface “... ad alcuno, dico, di quelli, che troppo laconicamente vorrebbero vedere, nei piu
angusti spazii che possibil fusse, ristretti i filosofici insegnamenti, sı che sempre si usasse …
angusti spazii che possibil fusse, ristretti i filosofici insegnamenti, sı che sempre si usasse …
Nonlinear inviscid damping near monotonic shear flows
AD Ionescu, H Jia - arXiv preprint arXiv:2001.03087, 2020 - arxiv.org
We prove nonlinear asymptotic stability of a large class of monotonic shear flows among
solutions of the 2D Euler equations in the channel $\mathbb {T}\times [0, 1] $. More …
solutions of the 2D Euler equations in the channel $\mathbb {T}\times [0, 1] $. More …
Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with Velocity and Boundary
J Chen, TY Hou - Communications in Mathematical Physics, 2021 - Springer
Inspired by the numerical evidence of a potential 3D Euler singularity by Luo-Hou 30, 31
and the recent breakthrough by Elgindi 11 on the singularity formation of the 3D Euler …
and the recent breakthrough by Elgindi 11 on the singularity formation of the 3D Euler …
Inviscid damping 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 …
* 0, 1 T× 0, 1. More precisely we prove that if we start with a small and smooth perturbation …
Finite time singularity for the modified SQG patch equation
It is well known that the incompressible Euler equations in two dimensions have globally
regular solutions. The inviscid surface quasi-geostrophic (SQG) equation has a Biot-Savart …
regular solutions. The inviscid surface quasi-geostrophic (SQG) equation has a Biot-Savart …