In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation e...In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.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
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
Based on the spectral decomposition for the linear and nonlinear radially symmetric homogeneous non-cutoff Landau operators under the hard potentialγ=2 in perturbation framework,we prove the existence and Gelfand-Shi...Based on the spectral decomposition for the linear and nonlinear radially symmetric homogeneous non-cutoff Landau operators under the hard potentialγ=2 in perturbation framework,we prove the existence and Gelfand-Shilov smoothing effect for solution to the Cauchy problem of the symmetric homogenous Landau equation with small initial datum.展开更多
基金supported by the NSFC(12101012)the PhD Scientific Research Start-up Foundation of Anhui Normal University.Zeng’s research was supported by the NSFC(11961160716,11871054,12131017).
文摘In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.
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the Fundamental Research Funds for the Central Universities of China,South-Central University for Nationalities(No.CZT20007)the Natural Science Foundation of China(No.11701578).
文摘Based on the spectral decomposition for the linear and nonlinear radially symmetric homogeneous non-cutoff Landau operators under the hard potentialγ=2 in perturbation framework,we prove the existence and Gelfand-Shilov smoothing effect for solution to the Cauchy problem of the symmetric homogenous Landau equation with small initial datum.
