Displaying similar documents to “Remarks on exact controllability for the Navier-Stokes equations”

Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class L ∞ ( 0 , T , L 3 ( Ω ) 3 )

Zdeněk Skalák (2003)

Applications of Mathematics

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We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution 𝐮 belongs to L ∞ ( 0 , T , L 3 ( Ω ) 3 ) , then the set of all possible singular points of 𝐮 in Ω is at most finite at every time t 0 ∈ ( 0 , T ) .

Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid

Jiří Neustupa (1988)

Aplikace matematiky

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The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is...

On the exterior problem in 2D for stationary flows of fluids with shear dependent viscosity

Michael Bildhauer, Martin Fuchs (2012)

Commentationes Mathematicae Universitatis Carolinae

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On the complement of the unit disk B we consider solutions of the equations describing the stationary flow of an incompressible fluid with shear dependent viscosity. We show that the velocity field u is equal to zero provided u | ∂ B = 0 and lim | x | → ∞ | x | 1 / 3 | u ( x ) | = 0 uniformly. For slow flows the latter condition can be replaced by lim | x | → ∞ | u ( x ) | = 0 uniformly. In particular, these results hold for the classical Navier-Stokes case.