32 citations · 147 across the 22 of their papers we have counts for
23 papers
Blow-up of dynamically restricted critical norms near a potential Navier-Stokes singularity
Tobias Barker, Pedro Gabriel Fernández-Dalgo, Christophe Prange
In this paper we develop new methods to obtain regularity criteria for the three-dimensional Navier-Stokes equations in terms of dynamically restricted endpoint critical norms: the…
On symmetry breaking for the Navier-Stokes equations
Tobias Barker, Christophe Prange, Jin Tan
Inspired by an open question by Chemin and Zhang about the regularity of the 3D Navier-Stokes equations with one initially small component, we investigate symmetry breaking and sym…
From concentration to quantitative regularity: a short survey of recent developments for the Navier-Stokes equations
Tobias Barker, Christophe Prange
In this short survey paper, we focus on some new developments in the study of the regularity or potential singularity formation for solutions of the 3D Navier-Stokes equations. Som…
Epsilon regularity for the Navier-Stokes equations via weak-strong uniqueness
Dallas Albritton, Tobias Barker, Christophe Prange
We give a new concise proof of a certain one-scale epsilon regularity criterion using weak-strong uniqueness for solutions of the Navier-Stokes equations with non-zero boundary con…
Localized smoothing and concentration for the Navier-Stokes equations in the half space
Dallas Albritton, Tobias Barker, Christophe Prange
We establish a local-in-space short-time smoothing effect for the Navier-Stokes equations in the half space. The whole space analogue, due to Jia and Šverák [JŠ14], is a central to…
Motion of several slender rigid filaments in a Stokes flow
Richard M. Höfer, Christophe Prange, Franck Sueur
We investigate the dynamics of several slender rigid bodies moving in a flow driven by the three-dimensional steady Stokes system in presence of a smooth background flow. More prec…
Large-scale regularity for the stationary Navier-Stokes equations over non-Lipschitz boundaries
Mitsuo Higaki, Christophe Prange, Jinping Zhuge
In this paper we address the large-scale regularity theory for the stationary Navier-Stokes equations in highly oscillating bumpy John domains. These domains are very rough, possib…
Mild criticality breaking for the Navier-Stokes equations
Tobias Barker, Christophe Prange
In this short paper we prove the global regularity of solutions to the Navier-Stokes equations under the assumption that slightly supercritical quantities are bounded. As a consequ…
Anisotropy and stratification effects in the dynamics of fast rotating compressible fluids
Edoardo Bocchi, Francesco Fanelli, Christophe Prange
The primary goal of this paper is to develop robust methods to handle two ubiquitous features appearing in the modeling of geophysical flows: (i) the anisotropy of the viscous stre…
Quantitative regularity for the Navier-Stokes equations via spatial concentration
Tobias Barker, Christophe Prange
This paper is concerned with quantitative estimates for the Navier-Stokes equations. First we investigate the relation of quantitative bounds to the behaviour of critical norms nea…
Regularity for the stationary Navier-Stokes equations over bumpy boundaries and a local wall law
Mitsuo Higaki, Christophe Prange
We investigate regularity estimates for the stationary Navier-Stokes equations above a highly oscillating Lipschitz boundary with the no-slip boundary condition. Our main result is…
Scale-invariant estimates and vorticity alignment for Navier-Stokes in the half-space with no-slip boundary conditions
Tobias Barker, Christophe Prange
This paper is concerned with geometric regularity criteria for the Navier-Stokes equations in with no-slip boundary condition, with the assumption th…
Localized smoothing for the Navier-Stokes equations and concentration of critical norms near singularities
Tobias Barker, Christophe Prange
This paper is concerned with two dual aspects of the regularity question of the Navier-Stokes equations. First, we prove a local in time localized smoothing effect for local energy…
On stability of blow-up solutions of the Burgers vortex type for the Navier-Stokes equations with a linear strain
Yasunori Maekawa, Hideyuki Miura, Christophe Prange
We study the three-dimensional Navier-Stokes equations in the presence of the axisymmetric linear strain, where the strain rate depends on time in a specific manner. It is known th…
Infinite energy solutions to the Navier-Stokes equations in the half-space and applications
Christophe Prange
This short note serves as an introduction to the papers arXiv:1711.01651 and arXiv:1711.04486 by Maekawa, Miura and Prange. These two works deal with the existence of mild solution…
Local energy weak solutions for the Navier-Stokes equations in the half-space
Yasunori Maekawa, Hideyuki Miura, Christophe Prange
The purpose of this paper is to prove the existence of global in time local energy weak solutions to the Navier-Stokes equations in the half-space . Such solutions a…
Estimates for the Navier-Stokes equations in the half-space for non localized data
Yasunori Maekawa, Hideyuki Miura, Christophe Prange
This paper is devoted to the study of the Stokes and Navier-Stokes equations, in a half-space, for initial data in a class of locally uniform Lebesgue integrable functions, namely…
Quantitative analysis of boundary layers in periodic homogenization
Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat +1
We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estim…
Improved Regularity in Bumpy Lipschitz Domains
Carlos Kenig, Christophe Prange
This paper is devoted to the proof of Lipschitz regularity, down to the microscopic scale, for solutions of an elliptic system with highly oscillating coefficients, over a highly o…
Uniform Lipschitz Estimates in Bumpy Half-Spaces
Carlos Kenig, Christophe Prange
This paper is devoted to the proof of uniform Hölder and Lipschitz estimates close to oscillating boundaries, for divergence form elliptic systems with periodically oscillating coe…
Well-posedness of the Stokes-Coriolis system in the half-space over a rough surface
Anne-Laure Dalibard, Christophe Prange
This paper is devoted to the well-posedness of the stationary d Stokes-Coriolis system set in a half-space with rough bottom and Dirichlet data which does not decrease at space…
Asymptotic analysis of boundary layer correctors in periodic homogenization
Christophe Prange
This paper is devoted to the asymptotic analysis of boundary layers in periodic homogenization. We investigate the behaviour of the boundary layer corrector, defined in the half-sp…
First-order expansion for the Dirichlet eigenvalues of an elliptic system with oscillating coefficients
Christophe Prange
This paper is concerned with the homogenization of the Dirichlet eigenvalue problem, posed in a bounded domain , for a vectorial elliptic operator $-\nabla\cdo…