The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Shuichi Kawashima - One of the best experts on this subject based on the ideXlab platform.
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asymptotic stability of rarefaction wave for the navier stokes equations for a compressible fluid in the half space
Archive for Rational Mechanics and Analysis, 2009Co-Authors: Shuichi KawashimaAbstract:This paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier–Stokes equations in a compressible fluid in the Eulerian Coordinate in the half space. This is the second one of our series of papers on this subject. In this paper, firstly we classify completely the time-asymptotic states, according to some parameters, that is the spatial-asymptotic states and boundary conditions, for this initial boundary value problem, and some pictures for the classification of time-asymptotic states are drawn in the state space. In order to prove the stability of the rarefaction wave, we use the solution to Burgers’ equation to construct a suitably smooth approximation of the rarefaction wave and establish some time-decay estimates in Lp-norm for the smoothed rarefaction wave. We then employ the L2-energy method to prove that the rarefaction wave is non-linearly stable under a small perturbation, as time goes to infinity.
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Asymptotic Stability of Rarefaction Wave for the Navier–Stokes Equations for a Compressible Fluid in the Half Space
Archive for Rational Mechanics and Analysis, 2008Co-Authors: Shuichi KawashimaAbstract:This paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier–Stokes equations in a compressible fluid in the Eulerian Coordinate in the half space. This is the second one of our series of papers on this subject. In this paper, firstly we classify completely the time-asymptotic states, according to some parameters, that is the spatial-asymptotic states and boundary conditions, for this initial boundary value problem, and some pictures for the classification of time-asymptotic states are drawn in the state space. In order to prove the stability of the rarefaction wave, we use the solution to Burgers’ equation to construct a suitably smooth approximation of the rarefaction wave and establish some time-decay estimates in Lp-norm for the smoothed rarefaction wave. We then employ the L2-energy method to prove that the rarefaction wave is non-linearly stable under a small perturbation, as time goes to infinity.
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Asymptotic stability of nonlinear wave for the compressible Navier-Stokes equations in the half space
Journal of Differential Equations, 2008Co-Authors: Shuichi Kawashima, Peicheng ZhuAbstract:In the present paper, we investigate the large-time behavior of the solution to an initial–boundary value problem for the isentropic compressible Navier–Stokes equations in the Eulerian Coordinate in the half space. This is one of the series of papers by the authors on the stability of nonlinear waves for the outflow problem of the compressible Navier–Stokes equations. Some suitable assumptions are made to guarantee that the time-asymptotic state is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave. Employing the L2-energy method and making use of the techniques from the paper [S. Kawashima, Y. Nikkuni, Stability of rarefaction waves for the discrete Boltzmann equations, Adv. Math. Sci. Appl. 12 (1) (2002) 327–353], we prove that this nonlinear wave is nonlinearly stable under a small perturbation. The complexity of nonlinear wave leads to many complicated terms in the course of establishing the a priori estimates, however those terms are of two basic types, and the terms of each type are “good” and can be evaluated suitably by using the decay (in both time and space variables) estimates of each component of nonlinear wave.
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asymptotic stability of the stationary solution to the compressible navier stokes equations in the half space
Communications in Mathematical Physics, 2003Co-Authors: Shuichi Kawashima, Shinya Nishibata, Peicheng ZhuAbstract:We investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible Navier–Stokes equation in a half space. The main concern is to analyze the phenomena that happens when the fluid blows out through the boundary. Thus, it is natural to consider the problem in the Eulerian Coordinate. We have obtained the two results for this problem. The first result is concerning the existence of the stationary solution. We present the necessary and sufficient condition which ensures the existence of the stationary solution. Then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable Sobolev space. The second result is proved by using an L 2 -energy method with the aid of the Poincare type inequality.
Yi Wang - One of the best experts on this subject based on the ideXlab platform.
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STABILITY OF VISCOUS SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY
2016Co-Authors: Feimin Huang, Xiaoding Shi, Yi WangAbstract:(Communicated by Tong Yang) Abstract. A free boundary problem for the one-dimensional compressible Navier-Stokes equations in Eulerian Coordinate is investigated. The stability of the viscous shock wave to the free boundary problem is established under some smallness conditions. The proof is given by an elementary energy method. 1. Introduction. W
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STABILITY OF SUPERPOSITION OF TWO VISCOUS SHOCK WAVES FOR THE BOLTZMANN EQUATION
SIAM Journal on Mathematical Analysis, 2015Co-Authors: Teng Wang, Yi WangAbstract:In this paper we study the time-asymptotic stability of a superposition of two viscous shock waves for one-dimensional Boltzmann equation in Eulerian Coordinate under the general initial perturbation without the zero total macroscopic mass condition. Roughly speaking, the general perturbation without the zero mass condition will generate not only the shifts on the two viscous shock waves, but also the linear diffusion wave in the linearly degenerate field. Furthermore, the coupled diffusion waves for the macroscopic part are also crucial in the stability analysis. By using the delicate weighted characteristic energy estimates based on the underlying wave structure, we succeed in proving the time-asymptotic stability of a superposition of two viscous shock waves for Boltzmann equation in Eulerian Coordinate without the zero initial mass condition.
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Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary
Kinetic & Related Models, 2010Co-Authors: Feimin Huang, Xiaoding Shi, Yi WangAbstract:A free boundary problem for the one-dimensional compressible Navier-Stokes equations in Eulerian Coordinate is investigated. The stability of the viscous shock wave to the free boundary problem is established under some smallness conditions. The proof is given by an elementary energy method.
Yi Zhu - One of the best experts on this subject based on the ideXlab platform.
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Global classical solutions of 3D viscous MHD system without magnetic diffusion on periodic boxes
'Springer Science and Business Media LLC', 2018Co-Authors: Pan Ronghua, Yi Zhou, Yi ZhuAbstract:In this paper, we study the global existence of classical solutions to the three dimensional incompressible viscous magneto-hydrodynamical system without magnetic diffusion on periodic boxes, i.e., with periodic boundary conditions. We work in Eulerian Coordinate and employ a time-weighted energy estimate to prove the global existence result, under the assumptions that the initial magnetic field is close enough to an equilibrium state and the initial data have some symmetries.Comment: 24 page
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Global classical solutions of 3D viscous MHD system without magnetic diffusion on periodic boxes
Archive for Rational Mechanics and Analysis, 2017Co-Authors: Ronghua Pan, Yi Zhou, Yi ZhuAbstract:In this paper, we study the global existence of classical solutions to the three dimensional incompressible viscous magneto-hydrodynamical system without magnetic diffusion on periodic boxes, i.e., with periodic boundary conditions. We work in Eulerian Coordinate and employ a time-weighted energy estimate to prove the global existence result, under the assumptions that the initial magnetic field is close enough to an equilibrium state and the initial data have some symmetries.
Shigenori Yanagi - One of the best experts on this subject based on the ideXlab platform.
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LARGE-TIME BEHAVIOR OF SPHERICALLY SYMMETRIC SOLUTIONS TO AN ISENTROPIC MODEL OF COMPRESSIBLE VISCOUS FLUID IN A FIELD OF POTENTIAL FORCES
Mathematical Models and Methods in Applied Sciences, 2004Co-Authors: Tohru Nakamura, Shinya Nishibata, Shigenori YanagiAbstract:We study the large-time behavior of a spherically symmetric motion of isentropic and compressible viscous gas in a field of potential force over an unbounded exterior domain in ℝn(n≥2). First, we show the unique existence of a stationary solution satisfying an adhesion boundary condition and a positive spatial asymptotic condition. Then, it is shown that the stationary solution becomes a time asymptotic state to the initial boundary value problem with the same boundary and spatial asymptotic conditions. Here, the initial data can be chosen arbitrarily large if it belongs to the suitable Sobolev space. Moreover, if the external force is attractive to the center of a sphere, it can also be taken arbitrarily large. The proof of the stability theorem is based on computations, executed by using the Lagrangian Coordinate. In the proof, it is the essential step to obtain the pointwise estimate for the density. It is derived through employing a representation formula of the density with the aid of the standard energy method. The Holder regularity of the initial data is also required for translating the results in the Lagrangian Coordinate to those in the Eulerian Coordinate.
Victor Steinberg - One of the best experts on this subject based on the ideXlab platform.
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Statistics of particle pair separations in the elastic turbulent flow of a dilute polymer solution
Europhysics Letters (EPL), 2004Co-Authors: Teodor Burghelea, Enrico Segre, Victor SteinbergAbstract:We investigate experimentally the statistics of a chaotic flow of a dilute polymer solution in a regime of elastic turbulence by using the Lagrangian Coordinates approach. We show that due to flow smoothness at small scales the Finite Time Lyapunov Exponent (FTLE) technique can be successfully used to investigate the statistics of particle pair separations at different scales. We compare the measured FTLE with the characteristics of statistical description in the Eulerian Coordinate presentation, namely the velocity correlation times and the average velocity gradients. We characterize the flow intermittency by measuring high-order moments of the statistics of the particle pair separations.
