Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity

Alexis Vasseur

Displaying similar documents to “Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity”

Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in $ℝ^{n}$

Reinhard Farwig, Hermann Sohr (2009)

Czechoslovak Mathematical Journal

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For a bounded domain $Ω \subset ℝ^{n}$ , $n \geq 3,$ we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system $- Δ u + u \cdot \nabla u + \nabla p = f$ , $div u = k$ , $u_{|_{\partial Ω}} = g$ with $u \in L^{q}$ , $q \geq n$ , and very general data classes for $f$ , $k$ , $g$ such that $u$ may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of...

Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system

Nana Pan, Jishan Fan, Yong Zhou (2021)

Applications of Mathematics

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We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in $ℝ^{3}$ . It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.

A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient

Stefano Bosia, Monica Conti, Vittorino Pata (2014)

Open Mathematics

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The incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.

On the regularity for solutions of the micropolar fluid equations

Elva Ortega-Torres, Marko Rojas-Medar (2009)

Rendiconti del Seminario Matematico della Università di Padova

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Some new regularity criteria for the Navier-Stokes equations containing gradient of the velocity

Patrick Penel, Milan Pokorný (2004)

Applications of Mathematics

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We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.

A short note on regularity criteria for the Navier-Stokes equations containing the velocity gradient

Milan Pokorný (2005)

Banach Center Publications

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We review several regularity criteria for the Navier-Stokes equations and prove some new ones, containing different components of the velocity gradient.

Regularity criterion for weak solutions to the Navier-Stokes equations in terms of the gradient of the pressure.

Fan, Jishan, Ozawa, Tohru (2008)

Journal of Inequalities and Applications [electronic only]

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Global regularity for the 3D inhomogeneous incompressible Navier-Stokes equations with damping

Kwang-Ok Li, Yong-Ho Kim (2023)

Applications of Mathematics

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This paper is concerned with the 3D inhomogeneous incompressible Navier-Stokes equations with damping. We find a range of parameters to guarantee the existence of global strong solutions of the Cauchy problem for large initial velocity and external force as well as prove the uniqueness of the strong solutions. This is an extension of the theorem for the existence and uniqueness of the 3D incompressible Navier-Stokes equations with damping to inhomogeneous viscous incompressible fluids. ...