In this work,we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework.We prove that the solution to the Cauchy problem enjoys the analytic regul...In this work,we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework.We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an L^(2)initial datum for positive time.So that the smoothing effect of the Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.展开更多
In this work,we study the Cauchy problem of the nonlinear spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework.We prove that the solution to the Cauchy problem with the initia...In this work,we study the Cauchy problem of the nonlinear spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework.We prove that the solution to the Cauchy problem with the initial datum in L^(2)enjoys an analytic regularizing effect,and the evolution of the analytic radius is the same as that of heat equations.展开更多
This paper is concerned with the construction of globally smooth solutions near a given global Maxwellian to the Cauchy problem of tile Vlasov-Poisson-Boltzmann system for non-cutoff hard potentials in three space dim...This paper is concerned with the construction of globally smooth solutions near a given global Maxwellian to the Cauchy problem of tile Vlasov-Poisson-Boltzmann system for non-cutoff hard potentials in three space dimensions without the neutral condition imposed on the initial perturbation. Our analysis is based on the time-weighted energy method and some delicate estimates.展开更多
基金the NSFC(No.12031006)and the Fundamental Research Funds for the Central Universities of China.
文摘In this work,we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework.We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an L^(2)initial datum for positive time.So that the smoothing effect of the Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.
基金supported by National Natural Science Foundation of China(Grant No.11701578)supported by National Natural Science Foundation of China(Grant No.12031006)+1 种基金the Fundamental Research Funds for the Central UniversitiesSouth-Central Minzu University(Grant No.CZT20007)。
文摘In this work,we study the Cauchy problem of the nonlinear spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework.We prove that the solution to the Cauchy problem with the initial datum in L^(2)enjoys an analytic regularizing effect,and the evolution of the analytic radius is the same as that of heat equations.
基金supported by National Natural Science Foundation of China(Grant Nos.10925103,11261160 and 11271160)the Fundamental Research Funds for the Central Universities
文摘This paper is concerned with the construction of globally smooth solutions near a given global Maxwellian to the Cauchy problem of tile Vlasov-Poisson-Boltzmann system for non-cutoff hard potentials in three space dimensions without the neutral condition imposed on the initial perturbation. Our analysis is based on the time-weighted energy method and some delicate estimates.
