Related papers: Higher Order Stability Analysis for Astrophysical …
Building on Evans function techniques developed to study the stability of viscous shocks, we examine the stability of viscous strong detonation wave solutions of the reacting Navier-Stokes equations. The primary result, following the work…
We study the stability of standing shock waves in advection-dominated accretion flows into a Schwarzschild black hole by 2D general relativistic hydrodynamic simulations as well as linear analysis in the equatorial plane. We demonstrate…
We examine the accretion of matter onto a black hole in scalar--tensor--vector gravity (STVG) also known as modified gravity (MOG). The gravitational constant is $G=G_{N} (1 + \alpha)$ where $\alpha$ is a parameter taken to be constant for…
In this chapter, I present a summary of observational tests of the basic picture of disk accretion. An emphasis is placed on tests relevant to black holes, but many of the fundamental results are drawn from studies of other classes of…
Analytical studies of black hole accretion usually presumes the stability of the stationary transonic configuration. Various authors in the past several decades demonstrated the validity of such an assumption for inviscid hydrodynamic flow.…
Generalizing similar results for viscous shock and relaxation waves, we establish sharp pointwise Green function bounds and linearized and nonlinear stability for traveling wave solutions of an abstract viscous combustion model including…
We consider the two-dimensional incompressible inhomogeneous Navier-Stokes equations with odd viscosity, where the shear and the odd viscosity coefficients depend continuously on the unknown density function. We establish the existence of…
An analytical theory is presented for linear, local, short-wavelength instabilities in swirling flows, in which axial shear, differential rotation, radial thermal stratification, viscosity, and thermal diffusivity are all taken into…
Physical experiments and numerical simulations have observed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and damps electrically conducting fluids. This paper intends to establish this phenomenon as a…
In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is…
We show the existence and the regularity properties of the weak solutions to the two-dimensional stationary incompressible inhomogeneous Navier-Stokes equations with variable viscosity coefficient, by analyzing a fourth-order nonlinear…
Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…
The inner boundary of a black hole accretion disk is often set to the marginally stable circular orbit (or the innermost stable circular orbit, ISCO) around the black hole. It is important for the theories of black hole accretion disks and…
This work aims to explore the gravitational consequences of a recently proposed black hole solution presented in the literature [Phys. Dark Univ. 50 (2025) 102061]. We initiate our analyzes by taking into account the horizon structure,…
We show a general stability result in the framework of strong solutions of the Navier-Stokes-Fourier system describing the motion of a compressible viscous and heat conducting gas. As a corollary, we develop a concept of statistical…
We consider the large time behavior of the three-dimensional Navier-Stokes flow around a rotating rigid body. Assume that the angular velocity of the body gradually increases until it reaches a small terminal one at a certain finite time…
This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet…
We propose a novel collocated projection method for solving the incompressible Navier-Stokes equations with arbitrary boundaries. Our approach employs non-graded octree grids, where all variables are stored at the nodes. To discretize the…
We study the steady-state Navier-Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For…
We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…