On the artificial compressibility method for the Navier-Stokes-Fourier system
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TLDR
In this paper, the authors deal with the artificial compressibility approximation method adapted to the incompressible Navier Stokes Fourier system, and two different types of approximations are analyzed: one for the full NSF system where viscous heating effects are considered and the other for when the dissipative function S: ∇u is omitted.Citations
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Leray weak solutions of the incompressible Navier Stokes system on exterior domains via the artificial compressibility method
TL;DR: In this paper, the Leray weak solutions of the incompressible Navier Stokes equation in an exterior domain were studied and the strong convergence analysis of the velocity field was achieved by using the associated Leray-Hodge decomposition.
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The artificial compressibility approximation for mhd equations in unbounded domain
TL;DR: In this paper, a method of approximation for the weak solutions of the incompressible magnetohydrodynamic equations (MHD) in unbounded domains is presented. But the method is not suitable for the case of weak MHD.
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On the spectrum for the artificial compressible system
TL;DR: It is proved that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion by variational method, then it is also stable as a solutions of the artificial compressible one for sufficiently small ϵ.
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Stability of Bifurcating Stationary Solutions of the Artificial Compressible System
TL;DR: It is proved that when a stationary bifurcation from a simple eigenvalue occurs, the range of $$\epsilon $$ϵ can be taken uniformly near the b ifurcation point to conclude the stability of the bIfurcating solution as a solution of the artificial compressible system.
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An interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system
TL;DR: In this article, the role of the extra force density f e = − 1 2 ( ∇ · v ) v in the adimensionalized system of partial differential equations is discussed.
References
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Book
Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals
Elias M. Stein,Timothy S Murphy +1 more
TL;DR: In this article, the authors introduce the Heisenberg group and describe the Maximal Operators and Maximal Averages and Oscillatory Integral Integrals of the First and Second Kind.
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Numerical solution of the Navier-Stokes equations
TL;DR: In this paper, a finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced, which is equally applicable to problems in two and three space dimensions.
Book
Navier-Stokes Equations
TL;DR: Schiff's base dichloroacetamides having the formula OR2 PARALLEL HCCl2-C-N ANGLE R1 in which R1 is selected from the group consisting of alkenyl, alkyl, alkynyl and alkoxyalkyl; and R2 is selected by selecting R2 from the groups consisting of lower alkylimino, cyclohexenyl-1 and lower alkynyl substituted cycloenenyl -1 as discussed by the authors.
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Compact sets in the spaceL p (O,T; B)
TL;DR: In this paper, a characterization of compact sets in Lp (0, T; B) is given, where 1⩽P⩾∞ and B is a Banach space.