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Akitaka Matsumura - One of the best experts on this subject based on the ideXlab platform.

  • asymptotic stability of combination of viscous contact wave with rarefaction waves for one dimensional Compressible Navier stokes system
    Archive for Rational Mechanics and Analysis, 2010
    Co-Authors: Feimin Huang, Akitaka Matsumura
    Abstract:

    We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional Compressible Navier–Stokes system for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for the Compressible Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is proved that for the one-dimensional Compressible Navier–Stokes system, the combination wave of a “viscous contact wave”, which corresponds to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave is suitably small. This result is proved by using elementary energy methods.

  • optimal decay rate of the Compressible Navier stokes poisson system in mathbb r 3
    Archive for Rational Mechanics and Analysis, 2010
    Co-Authors: Akitaka Matsumura, Guojing Zhang
    Abstract:

    The Compressible Navier–Stokes–Poisson (NSP) system is considered in \({\mathbb {R}^3}\) in the present paper, and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that the density of the NSP system converges to its equilibrium state at the same L2-rate \({(1+t)^{-\frac {3}{4}}}\) or L∞-rate (1 + t)−3/2 respectively as the Compressible Navier–Stokes system, but the momentum of the NSP system decays at the L2-rate \({(1+t)^{-\frac {1}{4}}}\) or L∞-rate (1 + t)−1 respectively, which is slower than the L2-rate \({(1+t)^{-\frac {3}{4}}}\) or L∞-rate (1 + t)−3/2 for Compressible Navier–Stokes system [Duan et al., in Math Models Methods Appl Sci 17:737–758, 2007; Liu and Wang, in Comm Math Phys 196:145–173, 1998; Matsumura and Nishida, in J Math Kyoto Univ 20:67–104, 1980] and the L∞-rate (1 + t)−p with \({p \in (1, 3/2)}\) for irrotational Euler–Poisson system [Guo, in Comm Math Phys 195:249–265, 1998]. These convergence rates are shown to be optimal for the Compressible NSP system.

  • stability of a composite wave of two viscous shock waves for the full Compressible Navier stokes equation
    Communications in Mathematical Physics, 2009
    Co-Authors: Feimin Huang, Akitaka Matsumura
    Abstract:

    In this paper we investigate the asymptotic stability of a composite wave consisting of two viscous shock waves for the full Compressible Navier-Stokes equation. By introducing a new linear diffusion wave special to this case, we successfully prove that if the strengths of the viscous shock waves are suitably small with same order and also the initial perturbations which are not necessarily of zero integral are suitably small, the unique global solution in time to the full Compressible Navier-Stokes equation exists and asymptotically tends toward the corresponding composite wave whose shifts (in space) of two viscous shock waves are uniquely determined by the initial perturbations. We then apply the idea to study a half space problem for the full Compressible Navier-Stokes equation and obtain a similar result.

  • optimal decay rate of the Compressible Navier stokes poisson system in r 3
    arXiv: Mathematical Physics, 2008
    Co-Authors: Akitaka Matsumura, Guojing Zhang
    Abstract:

    The Compressible Navier-Stokes-Poisson (NSP) system is considered in $R^3$ in the present paper and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that the density of the NSP system converges to its equilibrium state at the same $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ respectively as the Compressible Navier-Stokes system, but the momentum of the NSP system decays at the $L^2$-rate $(1+t)^{-\frac14}$ or $L^\infty$-rate $(1+t)^{-1}$ respectively, which is slower than the $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ for the Compressible Navier-Stokes system. These convergence rates are also shown to be optimal for the Compressible NSP system.

Feimin Huang - One of the best experts on this subject based on the ideXlab platform.

Yi Wang - One of the best experts on this subject based on the ideXlab platform.

  • stability of planar rarefaction wave to two dimensional Compressible Navier stokes equations
    Siam Journal on Mathematical Analysis, 2018
    Co-Authors: Linan Li, Yi Wang
    Abstract:

    It is well known that the rarefaction wave, one of the basic wave patterns of the hyperbolic conservation laws, is nonlinearly stable to the one-dimensional Compressible Navier--Stokes equations (cf. [A. Matsumura and K. Nishihara, Japan J. Appl. Math., 3 (1986), pp. 1--13; Comm. Math. Phys., 144 (1992), pp. 325--335; T.-P. Liu and Z. P. Xin, Comm. Math. Phys., 118 (1988), pp. 451--465; K. Nishihara, T. Yang, and H. Zhao, SIAM J. Math. Anal., 35 (2004), pp. 1561--1597]). In the present paper we proved the time-asymptotical nonlinear stability of the planar rarefaction wave to the two-dimensional Compressible and isentropic Navier--Stokes equations, which gives the first stability result of the planar rarefaction wave to the multidimensional system with physical viscosities.

  • stability of planar rarefaction wave to 3d full Compressible Navier stokes equations
    Archive for Rational Mechanics and Analysis, 2018
    Co-Authors: Linan Li, Teng Wang, Yi Wang
    Abstract:

    We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, Compressible Navier–Stokes equations with the heat-conductivities in an infinite long flat nozzle domain $${\mathbb{R} \times \mathbb{T}^2}$$ . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x2 and x3 and its interactions with the planar rarefaction wave in x1 direction.

  • stability of planar rarefaction wave to 3d full Compressible Navier stokes equations
    arXiv: Analysis of PDEs, 2018
    Co-Authors: Teng Wang, Yi Wang
    Abstract:

    We prove the time-asymptotic stability toward planar rarefaction wave for the three-dimensional full Compressible Navier-Stokes equations in an infinite long flat nozzle domain $\mathbb{R}\times\mathbb{T}^2$. Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial to overcome the difficulties due to the wave propagation along the transverse directions $x_2$ and $x_3$ and its interactions with the planar rarefaction wave in $x_1$ direction.

  • STABILITY OF VISCOUS SHOCK WAVE FOR Compressible Navier-STOKES EQUATIONS WITH FREE BOUNDARY
    2016
    Co-Authors: Feimin Huang, Xiaoding Shi, Yi Wang
    Abstract:

    (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

  • global well posedness of the cauchy problem of two dimensional Compressible Navier stokes equations in weighted spaces
    Journal of Differential Equations, 2013
    Co-Authors: Yi Wang, Quansen Jiu, Zhouping Xin
    Abstract:

    Abstract In this paper, we study the global well-posedness of classical solution to 2D Cauchy problem of the Compressible Navier–Stokes equations with large initial data and vacuum. It is proved that if the shear viscosity μ is a positive constant and the bulk viscosity λ is the power function of the density, that is, λ ( ρ ) = ρ β with β > 3 , then the 2D Cauchy problem of the Compressible Navier–Stokes equations on the whole space R 2 admits a unique global classical solution ( ρ , u ) which may contain vacuums in an open set of R 2 . Note that the initial data can be arbitrarily large to contain vacuum states. Various weighted estimates of the density and velocity are obtained in this paper and these self-contained estimates reflect the fact that the weighted density and weighted velocity propagate along with the flow.

Guojing Zhang - One of the best experts on this subject based on the ideXlab platform.

  • optimal decay rate of the non isentropic Compressible Navier stokes poisson system in r 3
    Journal of Differential Equations, 2011
    Co-Authors: Guojing Zhang, Changjiang Zhu
    Abstract:

    In this paper, the Compressible non-isentropic Navier–Stokes–Poisson (NSP) system is considered in R3 and the influences of internal electric field on the qualitative behaviors of solutions are analyzed. We observe that the electric field leads to the rotating phenomena in charge transport and reduces the speed of fluid motion, but it does not influence the transport of charge density and the heat diffusion. Indeed, we show that both density and temperature of the NSP system converge to their equilibrium state at the same rate (1+t)−34 as the non-isentropic Compressible Navier–Stokes system, but the momentum decays at the rate (1+t)−14, which is slower than the rate (1+t)−34 for the pure Compressible Navier–Stokes system. These convergence rates are also shown to be optimal for the non-isentropic Compressible NSP system.

  • optimal decay rate of the Compressible Navier stokes poisson system in mathbb r 3
    Archive for Rational Mechanics and Analysis, 2010
    Co-Authors: Akitaka Matsumura, Guojing Zhang
    Abstract:

    The Compressible Navier–Stokes–Poisson (NSP) system is considered in \({\mathbb {R}^3}\) in the present paper, and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that the density of the NSP system converges to its equilibrium state at the same L2-rate \({(1+t)^{-\frac {3}{4}}}\) or L∞-rate (1 + t)−3/2 respectively as the Compressible Navier–Stokes system, but the momentum of the NSP system decays at the L2-rate \({(1+t)^{-\frac {1}{4}}}\) or L∞-rate (1 + t)−1 respectively, which is slower than the L2-rate \({(1+t)^{-\frac {3}{4}}}\) or L∞-rate (1 + t)−3/2 for Compressible Navier–Stokes system [Duan et al., in Math Models Methods Appl Sci 17:737–758, 2007; Liu and Wang, in Comm Math Phys 196:145–173, 1998; Matsumura and Nishida, in J Math Kyoto Univ 20:67–104, 1980] and the L∞-rate (1 + t)−p with \({p \in (1, 3/2)}\) for irrotational Euler–Poisson system [Guo, in Comm Math Phys 195:249–265, 1998]. These convergence rates are shown to be optimal for the Compressible NSP system.

  • optimal decay rate of the Compressible Navier stokes poisson system in r 3
    arXiv: Mathematical Physics, 2008
    Co-Authors: Akitaka Matsumura, Guojing Zhang
    Abstract:

    The Compressible Navier-Stokes-Poisson (NSP) system is considered in $R^3$ in the present paper and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that the density of the NSP system converges to its equilibrium state at the same $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ respectively as the Compressible Navier-Stokes system, but the momentum of the NSP system decays at the $L^2$-rate $(1+t)^{-\frac14}$ or $L^\infty$-rate $(1+t)^{-1}$ respectively, which is slower than the $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ for the Compressible Navier-Stokes system. These convergence rates are also shown to be optimal for the Compressible NSP system.

Linan Li - One of the best experts on this subject based on the ideXlab platform.

  • vanishing viscosity limit to the planar rarefaction wave for the two dimensional full Compressible Navier stokes equations
    Journal of Differential Equations, 2020
    Co-Authors: Xing Li, Linan Li
    Abstract:

    Abstract The vanishing viscosity limit for the multi-dimensional Compressible Navier-Stokes equations to the corresponding Euler equations is a difficult and challenging problem in the mathematics. Recently, L.Li, D.Wang and Y.Wang [17] verified that the solutions for the 2D Compressible isentropic Navier-Stokes equations converge to the planar rarefaction wave solution for the corresponding 2D Euler equations as viscosity vanishes with a convergence rate ϵ 1 / 6 | ln ⁡ ϵ | . In this paper, the vanishing viscosity limit of 2D non-isentropic Compressible Navier-Stokes equations is studied. In contrast to the work [17] , the convergence rate for the 2D full Compressible Navier-Stokes equations is improved to ϵ 2 / 7 | ln ⁡ ϵ | 2 by choosing a different scaling argument and performing more detailed energy estimates.

  • stability of planar rarefaction wave to two dimensional Compressible Navier stokes equations
    Siam Journal on Mathematical Analysis, 2018
    Co-Authors: Linan Li, Yi Wang
    Abstract:

    It is well known that the rarefaction wave, one of the basic wave patterns of the hyperbolic conservation laws, is nonlinearly stable to the one-dimensional Compressible Navier--Stokes equations (cf. [A. Matsumura and K. Nishihara, Japan J. Appl. Math., 3 (1986), pp. 1--13; Comm. Math. Phys., 144 (1992), pp. 325--335; T.-P. Liu and Z. P. Xin, Comm. Math. Phys., 118 (1988), pp. 451--465; K. Nishihara, T. Yang, and H. Zhao, SIAM J. Math. Anal., 35 (2004), pp. 1561--1597]). In the present paper we proved the time-asymptotical nonlinear stability of the planar rarefaction wave to the two-dimensional Compressible and isentropic Navier--Stokes equations, which gives the first stability result of the planar rarefaction wave to the multidimensional system with physical viscosities.

  • stability of planar rarefaction wave to 3d full Compressible Navier stokes equations
    Archive for Rational Mechanics and Analysis, 2018
    Co-Authors: Linan Li, Teng Wang, Yi Wang
    Abstract:

    We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, Compressible Navier–Stokes equations with the heat-conductivities in an infinite long flat nozzle domain $${\mathbb{R} \times \mathbb{T}^2}$$ . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x2 and x3 and its interactions with the planar rarefaction wave in x1 direction.