m
• E

F Nous contacter

0

# Documents  Danchin, Raphaël | enregistrements trouvés : 8

O

P Q

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## The Onsager Theorem De Lellis, Camillo | CIRM H

Post-edited

Research talks;Partial Differential Equations;Mathematical Physics

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is.
Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics. Our remark sparked a series of discoveries and works which have gone in several directions. Among them the most notable is the recent proof of Phil Isett of a long-standing conjecture of Lars Onsager in the theory of turbulent flows. In a joint work with László, Tristan Buckmaster and Vlad Vicol we improve Isett's theorem to show the existence of dissipative solutions of the incompressible Euler equations below the Onsager's threshold.
In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is.
Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics. Our remark sparked a series of ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Mathematical analysis in fluid mechanics : selected recent results.International conference on vorticity, rotation and symmetry (IV) - complex fluids and the issue of regularityMarseille # May 8-12, 2017 Danchin, Raphaël ; Farwig, Reinhard ; Neustupa, Jiri ; Penel, Patrick | American Mathematical Society 2018

Congrès

- viii; 242 p.
ISBN 978-1-4704-3646-9

Contemporay mathematics , 0710

Localisation : Collection 1er étage

mécanique des fluides # équation de Navier-Stokes # fluide non-newtonien # magnétohydrodynamique (MHD) # mélange de fluides

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Recent approaches based on harmonic analysis for the study of non regular solutions to the Navier-Stokes equations with variable density Danchin, Raphaël | CIRM H

Multi angle

Research talks;Analysis and its Applications;Partial Differential Equations

The inhomogeneous incompressible Navier-Stokes equations that govern the evolution of viscous incompressible flows with non-constant density have received a lot of attention lately. In this talk, we shall mainly focus on the singular situation where the density is discontinuous, which is in particular relevant for describing the evolution of a mixture of two incompressible and non reacting fluids with constant density, or of a drop of liquid in vacuum. We shall highlight the places where tools in harmonic analysis play a key role, and present a few open problems. The inhomogeneous incompressible Navier-Stokes equations that govern the evolution of viscous incompressible flows with non-constant density have received a lot of attention lately. In this talk, we shall mainly focus on the singular situation where the density is discontinuous, which is in particular relevant for describing the evolution of a mixture of two incompressible and non reacting fluids with constant density, or of a drop of liquid in ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## $L^q$-$L^r$ estimates of a generalized Oseen evolution operator, with applications to the Navier-Stokes flow past a rotating obstacle Hishida, Toshiaki | CIRM H

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

Consider the motion of a viscous incompressible fluid in a 3D exterior domain $D$ when a rigid body $\mathbb R^3\setminus D$ moves with prescribed time-dependent translational and angular velocities. For the linearized non-autonomous system, $L^q$-$L^r$ smoothing action near $t=s$ as well as generation of the evolution operator $\{T(t,s)\}_{t\geq s\geq 0}$ was shown by Hansel and Rhandi [1] under reasonable conditions. In this presentation we develop the $L^q$-$L^r$ decay estimates of the evolution operator $T(t,s)$ as $(t-s)\to\infty$ and then apply them to the Navier-Stokes initial value problem. Consider the motion of a viscous incompressible fluid in a 3D exterior domain $D$ when a rigid body $\mathbb R^3\setminus D$ moves with prescribed time-dependent translational and angular velocities. For the linearized non-autonomous system, $L^q$-$L^r$ smoothing action near $t=s$ as well as generation of the evolution operator $\{T(t,s)\}_{t\geq s\geq 0}$ was shown by Hansel and Rhandi [1] under reasonable conditions. In this presentation we ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Large time behavior of solutions to 3-D MHD system with initial data near equilibrium Zhang, Ping | CIRM H

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

Given initial data $(b_0, u_0)$ close enough to the equilibrium state $(e_3, 0)$, we prove that the 3-D incompressible MHD system without magnetic diffusion has a unique global solution $(b, u)$. Moreover, we prove that $(b(t) - e_3, u(t))$ decay to zero with rates in both $L^\infty$ and $L^2$ norm. (This is a joint work with Wen Deng).

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## An asymptotic regime for the Vlasov-Poisson system Miot, Evelyne | CIRM H

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

We investigate the gyrokinetic limit for the two-dimensional Vlasov-Poisson system in a regime studied by F. Golse and L. Saint-Raymond. First we establish the convergence towards the Euler equation under several assumptions on the energy and on the norms of the initial data. Then we provide a first analysis of the asymptotics for a Vlasov-Poisson system describing the interaction of a bounded density with a moving point charge.

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## On the analysis of a class of thermodynamically compatible viscoelastic fluids with stress diffusion Málek, Josef | CIRM H

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

We first summarize the derivation of viscoelastic (rate-type) fluids with stress diffusion that generates the models that are compatible with the second law of thermodynamics and where no approximation/reduction takes place. The approach is based on the concept of natural configuration that splits the total response between the current and initial configuration into the purely elastic and dissipative part. Then we restrict ourselves to the class of fluids where elastic response is purely spherical. For such class of fluids we then provide a mathematical theory that, in particular, includes the long-time and large-data existence of weak solution for suitable initial and boundary value problems. This is a joint work with Miroslav Bulicek, Vit Prusa and Endre Suli. We first summarize the derivation of viscoelastic (rate-type) fluids with stress diffusion that generates the models that are compatible with the second law of thermodynamics and where no approximation/reduction takes place. The approach is based on the concept of natural configuration that splits the total response between the current and initial configuration into the purely elastic and dissipative part. Then we restrict ourselves to the class ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Fourier analysis and nonlinear partial differential equations Bahouri, Hajer ; Chemin, Jean-Yves ; Danchin, Raphaël | Springer 2011

Ouvrage

- xv; 523 p.
ISBN 978-3-642-16829-1

Grundlehren der mathematischen wissenschaften , 0343

Localisation : Collection 1er étage

décomposition de Littlewood-Paley # équation aux dérivées partielles non linéaire # équation de transport # équation de la chaleur # équation d'onde # équation de Schroedinger # mécanique des fluides # relativité générale

#### Filtrer

##### Codes MSC

Ressources Electroniques (Depuis le CIRM)

Books & Print journals

Recherche avancée

0
Z