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Conditions for the solvability of a nonlinear boundary value problem of the flow of a viscous fluid

100%
Studziński J.
Mathematica Applicanda
|
1985
|
tom 12
|
nr 24
PL
.
EN
The author presents a discussion of existence, uniqueness and convergence of finite difference approximations for Navier-Stokes equations with convection in a two-dimensional rectangle with sufficiently small data.
2
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A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient

51%
Bosia S., Conti M., Pata V.
Open Mathematics
|
2014
|
tom 12
|
nr 7
1015-1025
EN
The incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.
3
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Global existence for a one-dimensional model in gas dynamics

51%
Njamkepo S.
Applicationes Mathematicae
|
1996-1997
|
tom 24
|
nr 2
203-221
EN
We prove the existence of a global solution for a one-dimensio- nal Navier-Stokes system for a gas with internal capillarity.
4
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On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion

45%
Mucha P. B., Zajączkowski W.
Applicationes Mathematicae
|
2000
|
tom 27
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nr 3
319-333
EN
The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that $u\in W^{2,1}_r(\widetilde{{\mitΩ}}^T)$ with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the $L_p$-approach the Lagrangian coordinates must be used. We are looking for solutions with lowest possible regularity because this simplifies the proof and decreases the number of compatibility conditions.
5
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Global φ-attractor for a modified 3D Bénard system on channel-like domains

38%
Kapustyan O. V., Pankov A. V.
Nonautonomous Dynamical Systems
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2014
|
tom 1
EN
In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.
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