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Displaying similar documents to “On blow-up of solution for Euler equations”

Modelling of miscible liquids with the Korteweg stress

Ilya Kostin, Martine Marion, Rozenn Texier-Picard, Vitaly A. Volpert (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the...

Remarks on exact controllability for the Navier-Stokes equations

Oleg Yu. Imanuvilov (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain Ω with control distributed in a subdomain ω ⊂ Ω ⊂ ℝ n , n ∈ { 2 , 3 } . The result that we obtained in this paper is as follows. Suppose that v ^ ( t , x ) is a given solution of the Navier-Stokes equations. Let v 0 ( x ) be a given initial condition and ∥ v ^ ( 0 , · ) - v 0 ∥ < ε where ε is small enough. Then there exists a locally distributed control u , supp u ⊂ ( 0 , T ) × ω such that the solution v ( t , x ) of the Navier-Stokes equations: ...