THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS*

doi:10.1007/s10473-023-0617-2

Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (6): 2597-2614.doi: 10.1007/s10473-023-0617-2

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THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS^*

Haoguang LI^1,2,†, Chaojiang XU³

1. School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China;
2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles, MIIT, Nanjing 210016, China;
3. School of Mathematics and Key Laboratory of Mathematical MIIT, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2022-04-25 Revised:2023-05-20 Published:2023-12-08
Contact: †Haoguang LI, E-mail: lihaoguang@scuec.edu.cn
About author:Chaojiang XU, E-mail: xuchaojiang@nuaa.edu.cn
Supported by:
Li's research was supported by the Natural Science Foundation of Hubei Province, China (2022CFB444) and the Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA). Xu's research was supported by the NSFC (12031006) and the Fundamental Research Funds for the Central Universities of China.

Abstract

CLC Number:

35B65

Haoguang LI, Chaojiang XU. THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS^*[J].Acta mathematica scientia,Series B, 2023, 43(6): 2597-2614.

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[1] Alexandre R, Morimoto Y, Ukai S, et al.Uncertainty principle and kinetic equations. J Funct Anal, 2008, 255: 2013-2066
[2] Chen H, Li W X, Xu C J. Analytic smoothness effect of solutions for spatially homogeneous Landau eqaution. Journal of Differential Equations2010, 248: 77-94
[3] Chen H, Li W X, Xu C J. Propagation of Gevrey regularity for solutions of Landau equations. Kinetic and Related Models, 2008, 1: 355-368
[4] Chen H, Li W X, Xu C J. Gevrey regularity for solution of the spatially homogeneous Landau equation. Acta Mathematics Scientia, 2009, 29B: 673-686
[5] Degond P, Lemou M. Dispersion Relations for the Linearized Fokker-Planck Equation. Arch Rat Mech Anal, 1997, 138: 137-167
[6] Desvillettes L, Villani C. On the spatially homogeneous Landau equation for hard potentials. I. Existence, uniqueness and smoothness. Comm Partial Differential Equations, 2000, 25: 179-259
[7] Guo Y. The Landau equation in a periodic box. Comm Math Phys, 2002, 231: 391-434
[8] Lerner N, Morimoto Y, Pravda-Starov K, Xu C J. Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators. Kinet Relat Models, 2013, 6: 625-648
[9] Li H G. The Gelfand-Shilov smoothing effect for the radially symmetric homogeneous Landau equation with Shubin initial datum. Comptes Rendus Mathematique, 2018, 356: 613-625
[10] Li H G, Xu C J. Cauchy problem for the spatially homogeneous landau equation with shubin class initial datum and Gelfand-Shilov smoothing effect. SIAM J Math Anal, 2019, 51: 532-564
[11] Li H G, Xu C J.Analytic smoothing effect of the non-linear spatially homogeneous Landau equation with hard potentials. Science China Mathematics, 2022, 65: 2079-2098
[12] Morimoto Y, Xu C J. Ultra-analytic effect of Cauchy problem for a class of kinetic equations. Journal of Differential Equations, 2009, 247: 596-617
[13] Morimoto Y, Pravda-Starov K, Xu C J. A remark on the ultra-analytic smoothing properties of the spatially homogeneous Landau equation. Kinetic and Related Models, 2013, 6: 715-727
[14] Villani C. On the spatially homogeneous Landau equation for Maxwellian molecules. Mathematical Models and Methods in Applied Sciences, 1998, 8: 957-983

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THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS^*

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