Large Potential Forces Research Articles

Global well‐posedness of classical solutions to 3D compressible magnetohydrodynamic equations with large potential force

We consider the Cauchy problem of isentropic compressible magnetohydrodynamic equations with large potential force in . When the initial data (ρ0,u0,H0) is of small energy, we investigate the global well‐posedness of classical solutions where the flow density is allowed to contain vacuum states.

Stability of the Equilibrium to the Boltzmann Equation with Large Potential Force

The Boltzmann equation with external potential force exists a unique equilibrium—local Maxwellian. The author constructs the nonlinear stability of the equilibrium when the initial datum is a small perturbation of the local Maxwellian in the whole space ℝ3. Compared with the previous result [Ukai, S., Yang, T. and Zhao, H.-J., Global solutions to the Boltzmann equation with external forces, Anal. Appl. (Singap.), 3, 2005, 157–193], no smallness condition on the Sobolev norm H1 of the potential is needed in our arguments. The proof is based on the entropy-energy inequality and the L2 − L∞ estimates.

Stability of stationary solution for the compressible viscous magnetohydrodynamic equations with large potential force in bounded domain

In this paper, we consider the 3-D compressible viscous magnetohydrodynamic (MHD) equations with some large potential force in bounded rigid vessel. We firstly construct the non-constant stationary solutions of the compressible viscous MHD equations under suitable constitutive assumptions. Next, a critical energy identity is established to achieve a universal stability criterion of the stationary solution. In this case, the stationary solution is exponential stable for any large external potential force. Finally, we show the well-posedness of the initial boundary value problem for the compressible viscous MHD equations with the large potential force, provided that the prescribed initial data is close to the stationary solution. It implies that the set satisfying the stability criterion is not empty.

Hindlimb myology of the monk parakeet (Aves, Psittaciformes)

We studied the hindlimb myology of the monk parakeet (Myiopsitta monachus). Like all parrots, it has zygodactyl feet enabling perching, climbing, hanging, moving easily among trees, and handling food. Muscles were described and weighed, and physiological cross-sectional area (PCSA) of four flexors and one extensor was calculated. In comparison to other muscles, the M. tibialis cranialis and the M. fibularis brevis show increased development and high PCSA values, and therefore, large potential force production. Also, a large proportion of muscle mass was involved in flexing the digits. We hypothesize that these muscle traits are associated with the arboreal locomotion and food manipulation habits. In the monk parakeet, the M. extensor digitorum longus sends a branch to the hallux, and the connection between the M. flexor digitorum longus and the M. flexor hallucis longus is type I (Gadow's classification). We reaffirm the presence of the M. ambiens as a plesiomorphic condition that disappears in most members of the order. Among Psittaciformes, the M. fibularis brevis is stronger and the M. fibularis weaker in arboreal species than in basal terrestrial ones (e.g., Strigops).

The necessary conditions for the stability of steady motions of systems with constraints produced by large potential forces

The problem of the necessary conditions for the stability of steady motions for systems with constraints produced by large potential forces is investigated. An augmented matrix, similar to that arising under conditions when the restriction of quadratic forms to a linear manifold is sign-definite, is introduced to investigate the eigenvalues of the linearized system. The question of the correctness of the realization of unilateral constraints in special cases of zero reaction is discussed using an example.

The existence and stability of the equilibria of mechanical systems with constraints produced by large potential forces

A modification of Routh's theorem is investigated for systems with unilateral constraints produced by large potential forces, which enables steady motions to be found and the sufficient conditions for their stability to be investigated. The problem of an orbital “monkey bridge” is considered as an example.

Existence of Solutions of Stationary Compressible Navier–Stokes Equations with Large Force

In this paper, we consider the Navier–Stokes equations for isentropic, compressible flows of a polytropic gas in a bounded domain. The equations to be considered are obtained by scaling to dimensionless form and then replacing the density ρ by ρ+ε2ρ, where ε is a Mach number. The existence of solutions has been known only for small forces or large potential forces near a rest state. The aim of this paper is to give a proof of the existence of stationary compressible Navier–Stokes equations with large force, when the Mach number ε is small.

Steady compressible Navier-Stokes equations with large potential forces via a method of decomposition

We investigate the steady compressible Navier–Stokes equations near the equilibrium state v = 0, ρ = ρ0 (v the velocity, ρ the density) corresponding to a large potential force. We introduce a method of decomposition for such equations: the velocity field v is split into a non-homogeneous incompressible part u (div (ρ0u) = (0) and a compressible (irrotational) part ∇ϕ. In such a way, the original complicated mixed elliptic–hyperbolic system is split into several ‘standard’ equations: a Stokes-type system for u, a Poisson-type equation for ϕ and a transport equation for the perturbation of the density σ = ρ − ρ0. For ρ0 = const. (zero potential forces), the method coincides with the decomposition of Novotny and Padula [21]. To underline the advantages of the present approach, we give, as an example, a ‘simple’ proof of the existence of isothermal flows in bounded domains with no-slip boundary conditions. The approach is applicable, with some modifications, to more complicated geometries and to more complicated boundary conditions as we will show in forthcoming papers. © 1998 B.G. Teubner Stuttgart–John Wiley & Sons Ltd.

STEADY FLOWS OF VISCOUS COMPRESSIBLE FLUIDS IN EXTERIOR DOMAINS UNDER SMALL PERTURBATIONS OF GREAT POTENTIAL FORCES

We investigate the steady compressible flows in three-dimensional exterior domains, in R3 and [Formula: see text], under the action of small perturbations of large potential forces and zero velocity at infinity. We prove existence and uniqueness of solutions in L2-spaces, and study their regularity as well as the decay at infinity.