Linearized System

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Michel Normandin - One of the best experts on this subject based on the ideXlab platform.

  • closing international real business cycle models with restricted financial markets
    Journal of International Money and Finance, 2008
    Co-Authors: Martin Boileau, Michel Normandin
    Abstract:

    Several authors argue that international real business cycle (IRBC) models with incomplete financial markets offer a good explanation of the ranking of cross-country correlations. This conclusion is suspect, because it is based on an analysis of the near steady state dynamics using a Linearized System of equations. The baseline IRBC model with incomplete markets does not possess a unique deterministic steady state and, as a result, its linear System of difference equations is not stationary. We show that the ranking of cross-country correlations is robust to modifications that ensure a unique steady state and a stationary System of linear difference equations. We find, however, that the modifications affect the quantitative predictions of the model.

  • closing international real business cycle models with restricted financial markets
    Cahiers de recherche, 2005
    Co-Authors: Martin Boileau, Michel Normandin
    Abstract:

    Several authors argue that international real business cycle (IRBC) models with incomplete financial markets offer a good explanation of the ranking of cross-country correlations. Unfortunately, this conclusion is suspect, because it is commonly based on an analysis of the near steady state dynamics using a Linearized System of equations. The baseline IRBC model with incomplete financial markets does not possess a unique deterministic steady state and, as a result, its linear System of difference equations is not stationary. We show that the explanation of the ranking of cross-country correlations is robust to modifications that ensure a unique steady state and a stationary System of linear difference equations. We find, however, that the modifications affect the quantitative predictions regarding key macroeconomic variables.

Huijiang Zhao - One of the best experts on this subject based on the ideXlab platform.

  • negative sobolev spaces and the two species vlasov maxwell landau System in the whole space
    Journal of Functional Analysis, 2014
    Co-Authors: Yuanjie Lei, Huijiang Zhao
    Abstract:

    Abstract A global solvability result of the Cauchy problem of the two-species Vlasov–Maxwell–Landau System near a given global Maxwellian is established by employing an approach different than that of [2] . Compared with that of [2] , the minimal regularity index and the smallness assumptions we imposed on the initial data are weaker. Our analysis does not rely on the decay of the corresponding Linearized System and the Duhamel principle and thus it can be used to treat the one-species Vlasov–Maxwell–Landau System for the case of γ > − 3 and the one-species Vlasov–Maxwell–Boltzmann System for the case of − 1 γ ≤ 1 to deduce the global existence results together with the corresponding temporal decay estimates.

  • negative sobolev spaces and the two species vlasov maxwell landau System in the whole space
    arXiv: Analysis of PDEs, 2013
    Co-Authors: Yuanjie Lei, Huijiang Zhao
    Abstract:

    A global solvability result of the Cauchy problem of the two-species Vlasov-Maxwell-Landau System near a given global Maxwellian is established by employing an approach different than that of [5]. Compared with that of [5], the minimal regularity index and the smallness assumptions we imposed on the initial data are weaker. Our analysis does not rely on the decay of the corresponding Linearized System and the Duhamel principle and thus it can be used to treat the one-species Vlasov-Maxwell-Landau System for the case of $\gamma>-3$ and the one-species Vlasov-Maxwell-Boltzmann System for the case of $-1<\gamma\leq 1$ to deduce the global existence results together with the corresponding temporal decay estimates.

Martin Boileau - One of the best experts on this subject based on the ideXlab platform.

  • closing international real business cycle models with restricted financial markets
    Journal of International Money and Finance, 2008
    Co-Authors: Martin Boileau, Michel Normandin
    Abstract:

    Several authors argue that international real business cycle (IRBC) models with incomplete financial markets offer a good explanation of the ranking of cross-country correlations. This conclusion is suspect, because it is based on an analysis of the near steady state dynamics using a Linearized System of equations. The baseline IRBC model with incomplete markets does not possess a unique deterministic steady state and, as a result, its linear System of difference equations is not stationary. We show that the ranking of cross-country correlations is robust to modifications that ensure a unique steady state and a stationary System of linear difference equations. We find, however, that the modifications affect the quantitative predictions of the model.

  • closing international real business cycle models with restricted financial markets
    Cahiers de recherche, 2005
    Co-Authors: Martin Boileau, Michel Normandin
    Abstract:

    Several authors argue that international real business cycle (IRBC) models with incomplete financial markets offer a good explanation of the ranking of cross-country correlations. Unfortunately, this conclusion is suspect, because it is commonly based on an analysis of the near steady state dynamics using a Linearized System of equations. The baseline IRBC model with incomplete financial markets does not possess a unique deterministic steady state and, as a result, its linear System of difference equations is not stationary. We show that the explanation of the ranking of cross-country correlations is robust to modifications that ensure a unique steady state and a stationary System of linear difference equations. We find, however, that the modifications affect the quantitative predictions regarding key macroeconomic variables.

Yuanjie Lei - One of the best experts on this subject based on the ideXlab platform.

  • negative sobolev spaces and the two species vlasov maxwell landau System in the whole space
    Journal of Functional Analysis, 2014
    Co-Authors: Yuanjie Lei, Huijiang Zhao
    Abstract:

    Abstract A global solvability result of the Cauchy problem of the two-species Vlasov–Maxwell–Landau System near a given global Maxwellian is established by employing an approach different than that of [2] . Compared with that of [2] , the minimal regularity index and the smallness assumptions we imposed on the initial data are weaker. Our analysis does not rely on the decay of the corresponding Linearized System and the Duhamel principle and thus it can be used to treat the one-species Vlasov–Maxwell–Landau System for the case of γ > − 3 and the one-species Vlasov–Maxwell–Boltzmann System for the case of − 1 γ ≤ 1 to deduce the global existence results together with the corresponding temporal decay estimates.

  • negative sobolev spaces and the two species vlasov maxwell landau System in the whole space
    arXiv: Analysis of PDEs, 2013
    Co-Authors: Yuanjie Lei, Huijiang Zhao
    Abstract:

    A global solvability result of the Cauchy problem of the two-species Vlasov-Maxwell-Landau System near a given global Maxwellian is established by employing an approach different than that of [5]. Compared with that of [5], the minimal regularity index and the smallness assumptions we imposed on the initial data are weaker. Our analysis does not rely on the decay of the corresponding Linearized System and the Duhamel principle and thus it can be used to treat the one-species Vlasov-Maxwell-Landau System for the case of $\gamma>-3$ and the one-species Vlasov-Maxwell-Boltzmann System for the case of $-1<\gamma\leq 1$ to deduce the global existence results together with the corresponding temporal decay estimates.

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

  • global well posedness for Systems of hyperbolic parabolic composite type with center manifold
    Journal of Mathematical Analysis and Applications, 2020
    Co-Authors: Weike Wang
    Abstract:

    Abstract Concerning the global existence of classical solution to Systems of hyperbolic-parabolic composite type, a well-known general theory was established by Kawashima in [4] , where the dissipation condition (Kawashima-Shizuta condition) to the Linearized System plays a fundamental role. Recently, Systems with much weaker dissipations have attracted a lot of attentions, see [1] , [2] , [10] , [11] among others. The typical feature of this kind of System is that the corresponding Linearized System has one eigenvalue with the real part equals to zero. This violates the Kawashima-Shizuta stability conditions. In this paper, we develop a general global well-posedness theory for this kind of System. Moreover, as the applications of the general theory, several examples are given.

  • the pointwise estimates of solutions for euler equations with damping in multi dimensions
    Journal of Differential Equations, 2001
    Co-Authors: Weike Wang, Tong Yang
    Abstract:

    We study the time-asymptotic behavior of solutions for the isentropic Euler equations with damping in multi-dimensions. The global existence and pointwise estimates of the solutions are obtained. Furthermore, we obtain the optimal Lp, 1Linearized System and some energy estimates.

  • the pointwise estimates of diffusion wave for the navier stokes Systems in odd multi dimensions
    Communications in Mathematical Physics, 1998
    Co-Authors: Tai-ping Liu, Weike Wang
    Abstract:

    We study the dissipation of solutions of the isentropic Navier–Stokes equations in odd multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are obtained and shown to exhibit the generalized Huygen's principle. Our approach is based on the detailed analysis of the Green function of the Linearized System. This is used to study the coupling of nonlinear diffusion waves.