Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Christophe Prange"'
Publikováno v:
Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 39:647-704
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 stress tensor, (ii) stratification effects. We focus on the barotropic Nav
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::732af559687aa65c3ae07e50f91ca158
https://doi.org/10.4171/aihpc/16
https://doi.org/10.4171/aihpc/16
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 \v{S}ver\'ak [J\v{S}14], is a central tool in two of the authors' recent work on quantitative $L^3_x
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4f9e2c75b59985536baaf860b5b28c41
https://hal.archives-ouvertes.fr/hal-03502259
https://hal.archives-ouvertes.fr/hal-03502259
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 precisely we consider the limit where the thickness of these slender rigid
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8a4345a166f886500bf2c16ab5844691
https://hal.archives-ouvertes.fr/hal-03264956
https://hal.archives-ouvertes.fr/hal-03264956
Autor:
Christophe Prange, Tobias Barker
Publikováno v:
Barker, T & Prange, C 2021, ' Mild criticality breaking for the Navier-Stokes equations ', Journal of Mathematical Fluid Mechanics, vol. 23, 66 . https://doi.org/10.1007/s00021-021-00591-1
Journal of Mathematical Fluid Dynamics
Journal of Mathematical Fluid Dynamics, 2021, ⟨10.1007/s00021-021-00591-1⟩
Journal of Mathematical Fluid Dynamics
Journal of Mathematical Fluid Dynamics, 2021, ⟨10.1007/s00021-021-00591-1⟩
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 consequence, we prove that if a solution $u$ to the Navier-Stokes equations b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::80a0a51fa26ab9a56df925e444a65b31
https://purehost.bath.ac.uk/ws/files/241307116/mild_supercrit4.0.pdf
https://purehost.bath.ac.uk/ws/files/241307116/mild_supercrit4.0.pdf
Publikováno v:
Analysis & PDE
Analysis & PDE, Mathematical Sciences Publishers, 2020, ⟨10.2140/apde.2020.13.945⟩
Anal. PDE 13, no. 4 (2020), 945-1010
Analysis & PDE, Mathematical Sciences Publishers, 2020, ⟨10.2140/apde.2020.13.945⟩
Anal. PDE 13, no. 4 (2020), 945-1010
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 $L^q_{uloc,\sigma}(\R^d_+)$. We prove the analyticity of the Stokes se
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cc27b09fa8822de5e87a6b2ab6dcc08d
https://hal.archives-ouvertes.fr/hal-01915547
https://hal.archives-ouvertes.fr/hal-01915547
Autor:
Tobias Barker, Christophe Prange
Publikováno v:
Archive for Rational Mechanics and Analysis
Archive for Rational Mechanics and Analysis, Springer Verlag, 2020
Archive for Rational Mechanics and Analysis, Springer Verlag, 2020
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 solutions. More precisely, if the initial data restricted to the unit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::68797e9f9f01862b66bc38e7e8f08a70
https://hal.archives-ouvertes.fr/hal-02374652
https://hal.archives-ouvertes.fr/hal-02374652
Publikováno v:
Journal of Mathematical Fluid Mechanics
Journal of Mathematical Fluid Mechanics, Springer Verlag, 2019, ⟨10.1007/s00021-019-0450-5⟩
Journal of Mathematical Fluid Mechanics, Springer Verlag, 2019, ⟨10.1007/s00021-019-0450-5⟩
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 that the system admits solutions which blow up in finite time and whose
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fba2e46f968a2bb4062641e5b6db3af2
https://hal.archives-ouvertes.fr/hal-01915545
https://hal.archives-ouvertes.fr/hal-01915545
Autor:
Christophe Prange, Tobias Barker
Publikováno v:
Barker, T & Prange, C 2019, ' Scale-invariant estimates and vorticity alignment for Navier-Stokes in the half-space with no-slip boundary conditions ', Archive for Rational Mechanics and Analysis, vol. 235, pp. 881–926 . https://doi.org/10.1007/s00205-019-01435-z
Archive for Rational Mechanics and Analysis
Archive for Rational Mechanics and Analysis, Springer Verlag, 2019, ⟨10.1007/s00205-019-01435-z⟩
Archive for Rational Mechanics and Analysis
Archive for Rational Mechanics and Analysis, Springer Verlag, 2019, ⟨10.1007/s00205-019-01435-z⟩
This paper is concerned with geometric regularity criteria for the Navier-Stokes equations in $\mathbb{R}^3_{+}\times (0,T)$ with no-slip boundary condition, with the assumption that the solution satisfies the `ODE blow-up rate' Type I condition. Mor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0c1d317a8997d7b41eab8e9a72f4cf30
https://purehost.bath.ac.uk/ws/files/241307982/geometric_halfspace.pdf
https://purehost.bath.ac.uk/ws/files/241307982/geometric_halfspace.pdf
Publikováno v:
Communications in Mathematical Physics
Communications in Mathematical Physics, Springer Verlag, 2019, ⟨10.1007/s00220-019-03344-4⟩
Communications in Mathematical Physics, Springer Verlag, 2019, ⟨10.1007/s00220-019-03344-4⟩
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 $\mathbb R^3_+$. Such solutions are sometimes called Lemari\'e-Rieusset solutions in the whole space $\
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::64938f9b4d0eb87efd33891953abe461
http://hdl.handle.net/20.500.12278/9629
http://hdl.handle.net/20.500.12278/9629
Autor:
Mitsuo Higaki, Christophe Prange
Publikováno v:
Calculus of Variations and Partial Differential Equations
Calculus of Variations and Partial Differential Equations, Springer Verlag, 2020, 59 (4), pp.131. ⟨10.1007/s00526-020-01789-3⟩
Calculus of Variations and Partial Differential Equations, Springer Verlag, 2020, 59 (4), pp.131. ⟨10.1007/s00526-020-01789-3⟩
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 an improved Lipschitz regularity estimate at scales larger than the b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6c1798eaa482cf3b859f57fe25aae1a4