Outflow Problem Research Articles

Stationary solutions of outflow problem for full compressible Navier–Stokes–Poisson system: existence, stability and convergence rate

Stationary solutions of outflow problem for full compressible Navier–Stokes–Poisson system: existence, stability and convergence rate

Asymptotic Stability of a Boundary Layer and Rarefaction Wave for the Outflow Problem of the Heat-Conductive Ideal Gas without Viscosity

This article is devoted to studying the initial-boundary value problem for an ideal polytropic model of non-viscous and compressible gas. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and give a rigorous proof of the asymptotic stability of both the degenerate boundary layer and its superposition with the 3-rarefaction wave under some smallness conditions. New weighted energy estimates are introduced, and the trace of the density and velocity on the boundary are handled by some subtle analysis. The decay properties of the boundary layer and the smooth rarefaction wave also play an important role.

In-Flow and Out-Flow Problem for the Stokes System

We investigate the existence and regularity of solutions to the stationary Stokes system and non-stationary Navier–Stokes equations in three dimensional bounded domains with in- and out-lets. We assume that on the in- and out-flow parts of the boundary the pressure is prescribed and the tangential component of the velocity field is zero, whereas on the lateral part of the boundary the fluid is at rest.

Asymptotic stability of the stationary solution to an out-flow problem for the Navier–Stokes–Korteweg equations of compressible fluids

We shall investigate the large-time behavior of solutions to an out-flow problem in one-dimensional half space for the Navier–Stokes–Korteweg equations which models compressible fluids with internal capillarity. Applying the center manifold theory, we prove the existence of the stationary solution under a smallness condition on the boundary data and a proper relation between the capillary coefficient κ and Mach number M+ at far field. Then making use of the energy method and the inequality of Poincaré type, we show that the stationary solution is asymptotically stable under smallness assumptions on the boundary data and the initial perturbation in Sobolev space.

Modified Pulat’s algorithm for the maximum outflow problem in undirected generalized networks

A generalized network is characterized by arc multipliers that specify which portion of the flow entering an arc at its tail node reaches its head node. In this paper, the goal is to maximize the flow excess at the sink in undirected generalized networks. We show that the results of the directed networks are not satis ed here. We have speci cally stated and proved the optimality conditions of the problem. We have also designed an algorithm according to Pulat's algorithm and achieved an efficient version.

Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line

<p style='text-indent:20px;'>In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the one-dimensional compressible isentropic micropolar fluid model in a half line <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}_{+}: = (0, \infty). $\end{document}</tex-math></inline-formula> We mainly investigate the unique existence, the asymptotic stability and convergence rates of stationary solutions to the outflow problem for this model. We obtain the convergence rates of global solutions towards corresponding stationary solutions if the initial perturbation belongs to the weighted Sobolev space. The proof is based on the weighted energy method by taking into account the effect of the microrotational velocity on the viscous compressible fluid.

Non-degenerate stationary solution for outflow problem on the 1-D viscous heat-conducting gas with radiation

Non-degenerate stationary solution for outflow problem on the 1-D viscous heat-conducting gas with radiation

Stationary solutions to outflow problem for 1-D compressible fluid models of Korteweg type: Existence, stability and convergence rate

In this paper, we are concerned with the outflow problem in the half line (0,∞) to the isothermal compressible Navier–Stokes–Korteweg system with a nonlinear boundary condition for vanishing capillary tensor at x=0. We first give some necessary and sufficient conditions for the existence of the stationary solutions with the aid of center manifold theory. We also show the stability of the stationary solutions under smallness assumptions on the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solutions is obtained, provided that the initial perturbations belong to the weighted Sobolev spaces.

Convergence rate of solutions toward stationary solutions to a two-phase model with magnetic field in a half line

In this paper, we study an asymptotic behavior of a solution to the outflow problem for a two-phase model with magnetic field. Our idea mainly comes from [1] and [2] which investigate the asymptotic stability and convergence rates of stationary solutions to the outflow problem for an isentropic Navier–Stokes equation. For the two-phase model with magnetic field, we also obtain the asymptotic stability and convergence rates of global solutions towards corresponding stationary solutions if the initial perturbation belongs to the weighted Sobolev space. The proof is based on the weighted energy method.

Converge rates towards stationary solutions for the outflow problem of planar magnetohydrodynamics on a half line

AbstractIn this paper, convergence rates of solutions towards stationary solutions for the outflow problem of planar magnetohydrodynamics (MHD) are investigated. Inspired by the relationship between MHD and Navier-Stokes, we prove that the global solutions of the planar MHD converge to the corresponding stationary solutions of Navier-Stokes equations. We obtain the corresponding convergence rates based on the weighted energy method when the initial perturbation belongs to some weighted Sobolev space.

Stability of Boundary Layer to An Outflow Problem for A Compressible Non-Newtonian Fluid in the Half Space

This paper investigates the large-time behavior of solutions to an outflow problem for a compressible non-Newtonian fluid in a half space. The main concern is to analyze the phenomena that happens when the compressible non-Newtonian fluid blows out through the boundary. Based on the existence of the stationary solution, it is proved that there exists a boundary layer (i.e., the stationary solution) to the outflow problem and the boundary layer is nonlinearly stable under small initial perturbation.

Convergence rate of stationary solutions to outflow problem for full Navier–Stokes equations

ABSTRACTThis paper is concerned with the large-time behavior of solutions to the outflow problem of full compressible Navier–Stokes equations for the general gas including ideal polytropic gas in the half line , where the gas flows out through the boundary. We first give some necessary and sufficient conditions for the existence of the stationary solution with the aid of center manifold theory. We also show the time asymptotic stability of the nondegenerate stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the exponential and algebraic decay of the solution toward the supersonic stationary solution is obtained, provided that the initial perturbation belongs to the Sobolev space with exponential and algebraic weight respectively.

Asymptotics toward a nonlinear wave for an outflow problem of a model of viscous ions motion

We shall investigate the asymptotic stability, toward a nonlinear wave, of the solution to an outflow problem for the one-dimensional compressible Navier–Stokes–Poisson equations. First, we construct this nonlinear wave which, under suitable assumptions, is the superposition of a stationary solution and a rarefaction wave. Then it is shown that the nonlinear wave is asymptotically stable in the case that the initial data are a suitably small perturbation of the nonlinear wave. The main ingredient of the proof is the [Formula: see text]-energy method that takes into account both the effect of the self-consistent electrostatic potential and the spatial decay of the stationary part of the nonlinear wave.

Existence and stability of stationary solution to compressible Navier–Stokes–Poisson equations in half line

In this paper, we investigate the asymptotic stability of the stationary solution to the outflow problem for the compressible Navier–Stokes–Poisson system in a half line. We show the existence of the stationary solution with the aid of the stable manifold theory. The time asymptotic stability of the stationary solution is obtained by the elementary energy method. Furthermore, for the supersonic flow at spatial infinity, we also obtain an algebraic and an exponential decay rate, when the initial perturbation belongs to the corresponding weighted Sobolev space. The proof is based on a time and space weighted energy method.

Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half-space

We study the large-time behavior of solutions to the compressible Navier–Stokes equations for a viscous and heat-conducting ideal polytropic gas in the one-dimensional half-space. A rarefaction wave and its superposition with a non-degenerate stationary solution are shown to be asymptotically stable for the outflow problem with large initial perturbation and general adiabatic exponent.

The stability of stationary solution for outflow problem on the navier-stokes-poisson system

In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.

Stability of the superposition of boundary layer and rarefaction wave for outflow problem on the two-fluid Navier–Stokes–Poisson system

This paper is concerned with the study of nonlinear stability of superposition of boundary layer and rarefaction wave on the two-fluid Navier–Stokes–Poisson system in the half line R+=:(0,+∞). On account of the quasineutral assumption and the absence of the electric field for the large time behavior, we successfully construct the boundary layer and rarefaction wave, and then we give the rigorous proofs of the stability theorems on the superposition of boundary layer and rarefaction wave under small perturbations for the corresponding initial boundary value problem of the Navier–Stokes–Poisson system, only provided the strength of boundary layer is small while the strength of rarefaction wave can be arbitrarily large. The complexity of nonlinear composite wave leads to many complicated terms in the course of establishing the a priori estimates. The proofs are given by an elementary L2 energy method.

Stability of stationary solutions to the outflow problem for full compressible Navier–Stokes equations with large initial perturbation

We investigate the large-time behavior of solutions to an outflow problem of the compressible Navier–Stokes equations for viscous and heat-conducting ideal polytropic gases in the half line. The non-degenerate stationary solution is shown to be asymptotically stable under large initial perturbation with no restriction on the adiabatic exponent, provided that the boundary strength is sufficiently small. The proofs are based on the nonlinear energy estimates and the crucial step is to obtain positive lower and upper bounds of the density and the temperature uniformly in time and space.

A new run-up algorithm based on local high-order analytic expansions

The practically important problem of the wave run-up is studied in this article in the framework of Nonlinear Shallow Water Equations (NSWE). The main novelty consists in the usage of high order local asymptotic analytical solutions in the vicinity of the shoreline. Namely, we use the analytical techniques introduced by S. Kovalevskaya and the analogy with the compressible gas dynamics (i.e. gas outflow problem into the vacuum). Our run-up algorithm covers all the possible cases of the wave slope on the shoreline and it incorporates the new analytical information in order to determine the shoreline motion to higher accuracy. The application of this algorithm is illustrated in several important practical examples. Finally, the simulation results are compared with the well-known analytical and experimental predictions.

Linking Essential Tremor to the Cerebellum: Clinical Evidence.

Essential tremor (ET) might be a family of diseases unified by the presence of kinetic tremor, but also showing etiological, pathological, and clinical heterogeneity. In this review, we will describe the most significant clinical evidence, which suggests that ET is linked to the cerebellum. Data for this review were identified by searching PUBMED (January 1966 to May 2015) crossing the terms "essential tremor" (ET) and "cerebellum," which yielded 201 entries, 11 of which included the term "cerebellum" in the article title. This was supplemented by articles in the author's files that pertained to this topic. The wide spectrum of clinical features of ET that suggest that it originates as a cerebellar or cerebellar outflow problem include the presence of intentional tremor, gait and balance abnormalities, subtle features of dysarthria, and oculomotor abnormalities, as well as deficits in eye-hand coordination, motor learning deficits, incoordination during spiral drawing task, abnormalities in motor timing and visual reaction time, impairment of social abilities, improvement in tremor after cerebellar stroke, efficacy of deep brain stimulation (which blocks cerebellar outflow), and cognitive dysfunction. It is unlikely, however, that cerebellar dysfunction, per se, fully explains ET-associated dementia, because the cognitive deficits that have been described in patients with cerebellar lesions are generally mild. Overall, a variety of clinical findings suggest that in at least a sizable proportion of patients with ET, there is an underlying abnormality of the cerebellum and/or its pathways.