Steady States of Self-Gravitating Incompressible Fluid in Two Dimensions
نویسنده
چکیده
In this paper we develop a simple model for the steady state of two-dimensional self-gravitating incompressible gas which is based on the hydrodynamic equations for stratified fluid. These equations are then reduced to a system of two equations for the mass density and the gravitational field. Analytical analysis and numerical solutions of these equations under different modeling assumptions ͑with special attention to the isothermal case͒ are then used to study the structure of the resulting steady state of the fluid.
منابع مشابه
Equilibrium configurations of fluids and their stability in higher dimensions
We study equilibrium shapes, stability and possible bifurcation diagrams of fluids in higher dimensions, held together by either surface tension or self-gravity. We consider the equilibrium shape and stability problem of self-gravitating spheroids, establishing the formalism to generalize the MacLaurin sequence to higher dimensions. We show that such simple models, of interest on their own, als...
متن کاملLocal stability criterion for self-gravitating disks in modified gravity
We study local stability of self-gravitating fluid and stellar disk in the context of modified gravity theories which predict a Yukawa-like term in the gravitational potential of a point mass. We investigate the effect of such a Yukawa-like term on the dynamics of self-gravitating disks. More specifically, we investigate the consequences of the presence of this term for the local stability of t...
متن کاملOn Local Existence of Solutions of the Free Boundary Problem for an Incompressible Viscous Self-gravitating Fluid Motion
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 ∈W 2,1 r (Ω̃ T ) with r > 3. The existence is proved by the method of successive approximations where the solvability of the Cauchy– Neumann problem for the Stok...
متن کاملStructure of Steady States for Streater’s Energy-transport Models of Gravitating Particles
Energy-transport models introduced by R. F. Streater describe the evolution of the density and temperature of a cloud of self-gravitating particles. We study the existence of steady states with prescribed mass and energy for these models.
متن کاملStudy and Analysis of Flow of an In-compressible Fluid past an Obstruction
In present work, the time independent laminar flow of a viscous, incompressible fluid in two dimensions flow has been studied. The fluid had been allowed to flow in a channel with an obstruction which was a rectangular plate of definite dimensions. The flow of water had been considered to be steady with uniform incident velocity with various boundary conditions. The resulting NavierStokes equat...
متن کامل