Equation de Navier-Stokes avec densité et viscosité variables dans l'espace critique

By Hammadi Abidi. 2007

138 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/ef7dd16fc512a75e2c54724591b3598ddf82edd7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Global solutions to 2-d inhomogeneous navier-stokes system with general velocity (2012, background): “It is easy to check that the norm of B d p p,1(R d)×B −1+ d p p,1 (R d) is scaling invariant under the scaling transformation (a0, u0)ℓ given by (1.3).”
Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids (2010, background): “Bony (see [4]) and rewrite on a generalized form in [1] by H.”
Global solutions to the 3-D incompressible inhomogeneous Navier–Stokes system (2012, unknown): “In [1], Abidi proved that if 1 < p < 2N , 0 < μ < μ̃(a), u0 ∈ B N p −1 p,1 (R ) and a0 ∈ B N p p,1(R ), then (INS) has a global solution provided that ‖a0‖ B N p p,1 +‖u0‖ B N p −1 p,1 c0 for some c0 sufficiently small.”
Global smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with variable viscosity (2009, methodology): “In [1], Abidi proved in general space dimension N that if 1 < p < 2N, 0 < μ < μ(ρ), u0 ∈ Ḃ N p −1 p,1 (R N ) and a0 = 1 ρ0 − 1 ∈ Ḃ N p p,1(R N ), then (INS) has a global solution provided that ‖a0‖ Ḃ N p p,1 +‖u0‖ Ḃ N p −1 p,1 ≤ c0 for c0 sufficiently small.”
Global Well-posedness of Incompressible Inhomogeneous Fluid Systems with Bounded Density or Non-Lipschitz Velocity (2012, background): “Abidi [1] proved that if 1 < p < 2d, 0 < μ < μ̃(a), u0 ∈ Ḃ d p −1 p,1 (R ) and a0 ∈ Ḃ d p p,1(R ), then (1.”
Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density (2013, background): “In this framework, it has been stated in [1, 7] that for the initial data (ρ0, u0) satisfying (ρ0 − 1) ∈ Ḃ d p p,1(R ), u0 ∈ Ḃ d p −1 p,1 (R ) with div u0 = 0 and that for a small enough constant c ‖ρ0 − 1‖ Ḃ d p p,1 + ‖u0‖ Ḃ d p−1 p,1 ≤ c, we have for any p ∈ [1, 2d) • existence of global solution ”
Global well‐posedness for compressible Navier‐Stokes equations with highly oscillating initial velocity (2009, unknown): “If φε(x) def == ei x1 ε φ(x), then for any ε > 0, ‖φε‖ Ḃ n 2 −1, n p −1 2,p ≤ Cε1− n p , here C is a constant independent of ε. Proof.”
A Lagrangian Approach for the Incompressible Navier‐Stokes Equations with Variable Density (2011, methodology): “[1, 2, 6, 7]) we want to solve the above system in critical homogeneous Besov spaces.”