Existence and stability theorems for abstract parabolic equations, and some of their applications

Gerhard Ströhmer; Wojciech Zajączkowski

Displaying similar documents to “Existence and stability theorems for abstract parabolic equations, and some of their applications”

Trapping regions and an ODE-type proof of the existence and uniqueness theorem for Navier-Stokes equations with periodic boundary conditions on the plane.

Zgliczyński, Piotr (2003)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Convergence of the rotating fluids system in a domain with rough boundaries

David Gérard-Varet (2003)

Journées équations aux dérivées partielles

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We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size $ϵ$ . We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as $ϵ$ goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with...

Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes

Isabelle Gallagher, Dragoş Iftimie, Fabrice Planchon (2002)

Journées équations aux dérivées partielles

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We study a priori global strong solutions of the incompressible Navier-Stokes equations in three space dimensions. We prove that they behave for large times like small solutions, and in particular they decay to zero as time goes to infinity. Using that result, we prove a stability theorem showing that the set of initial data generating global solutions is open.

Some stability results for reactive Navier-Stokes-Poisson systems

B. Ducomet (2000)

Banach Center Publications

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We review the main results concerning the global existence and the stability of solutions for some models of viscous compressible self-gravitating fluids used in classical astrophysics.

On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable

Eduard Feireisl (2001)

Commentationes Mathematicae Universitatis Carolinae

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We show compactness of bounded sets of weak solutions to the isentropic compressible Navier-Stokes equations in three space dimensions under the hypothesis that the adiabatic constant $γ > 3 / 2$ .

Spatial smoothness of the stationary solutions of the 3D Navier-Stokes equations.

Odasso, Cyril (2006)

Electronic Journal of Probability [electronic only]

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Some remarks to the compactness of steady compressible isentropic Navier-Stokes equations via the decomposition method

Antonín Novotný (1996)

Commentationes Mathematicae Universitatis Carolinae

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In [18]–[19], P.L. Lions studied (among others) the compactness and regularity of weak solutions to steady compressible Navier-Stokes equations in the isentropic regime with arbitrary large external data, in particular, in bounded domains. Here we investigate the same problem, combining his ideas with the method of decomposition proposed by Padula and myself in [29]. We find the compactness of the incompressible part $u$ of the velocity field $v$ and we give a new proof of the compactness...