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

Reinhard Farwig; Hermann Sohr

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

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

Alexis Vasseur (2009)

Applications of Mathematics

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In this short note we give a link between the regularity of the solution $u$ to the 3D Navier-Stokes equation and the behavior of the direction of the velocity $u / | u |$ . It is shown that the control of $Div (u / | u |)$ in a suitable $L_{t}^{p} (L_{x}^{q})$ norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based...

Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence

R. Farwig, H. Kozono, H. Sohr (2011)

Rendiconti del Seminario Matematico della Università di Padova

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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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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.

Remarks on the smoothness of the $L^{\infty} (0, T; L^{3})$ solutions of the 3-D Navier-Stokes equations.

Beirão da Veiga, H. (1997)

Portugaliae Mathematica

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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.

Displaying similar documents to “Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in ℝ n ”

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

Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence

On the regularity for solutions of the micropolar fluid equations

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

Remarks on the smoothness of the L ∞ ( 0 , T ; L 3 ) solutions of the 3-D Navier-Stokes equations.

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

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

Remarks on the smoothness of the $L^{\infty} (0, T; L^{3})$ solutions of the 3-D Navier-Stokes equations.