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A review of Boltzmann equation with singular kernels
Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation
1. | Université de Rouen, UMR 6085-CNRS, Mathématiques, Avenue de l’Université, BP.12, 76801 Saint Etienne du Rouvray, France |
[1] |
Léo Glangetas, Hao-Guang Li, Chao-Jiang Xu. Sharp regularity properties for the non-cutoff spatially homogeneous Boltzmann equation. Kinetic and Related Models, 2016, 9 (2) : 299-371. doi: 10.3934/krm.2016.9.299 |
[2] |
Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. Uniqueness of solutions for the non-cutoff Boltzmann equation with soft potential. Kinetic and Related Models, 2011, 4 (4) : 919-934. doi: 10.3934/krm.2011.4.919 |
[3] |
Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried, Semjon Vugalter. Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction. Kinetic and Related Models, 2017, 10 (4) : 901-924. doi: 10.3934/krm.2017036 |
[4] |
Léo Glangetas, Mohamed Najeme. Analytical regularizing effect for the radial and spatially homogeneous Boltzmann equation. Kinetic and Related Models, 2013, 6 (2) : 407-427. doi: 10.3934/krm.2013.6.407 |
[5] |
Renjun Duan, Shuangqian Liu, Tong Yang, Huijiang Zhao. Stability of the nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff potentials. Kinetic and Related Models, 2013, 6 (1) : 159-204. doi: 10.3934/krm.2013.6.159 |
[6] |
Milana Pavić-Čolić, Maja Tasković. Propagation of stretched exponential moments for the Kac equation and Boltzmann equation with Maxwell molecules. Kinetic and Related Models, 2018, 11 (3) : 597-613. doi: 10.3934/krm.2018025 |
[7] |
Hao Tang, Zhengrong Liu. On the Cauchy problem for the Boltzmann equation in Chemin-Lerner type spaces. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 2229-2256. doi: 10.3934/dcds.2016.36.2229 |
[8] |
Zhaohui Huo, Yoshinori Morimoto, Seiji Ukai, Tong Yang. Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff. Kinetic and Related Models, 2008, 1 (3) : 453-489. doi: 10.3934/krm.2008.1.453 |
[9] |
Lingbing He, Yulong Zhou. High order approximation for the Boltzmann equation without angular cutoff. Kinetic and Related Models, 2018, 11 (3) : 547-596. doi: 10.3934/krm.2018024 |
[10] |
Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : 187-212. doi: 10.3934/dcds.2009.24.187 |
[11] |
Ralf Kirsch, Sergej Rjasanow. The uniformly heated inelastic Boltzmann equation in Fourier space. Kinetic and Related Models, 2010, 3 (3) : 445-456. doi: 10.3934/krm.2010.3.445 |
[12] |
Amit Einav. On Villani's conjecture concerning entropy production for the Kac Master equation. Kinetic and Related Models, 2011, 4 (2) : 479-497. doi: 10.3934/krm.2011.4.479 |
[13] |
V. Varlamov, Yue Liu. Cauchy problem for the Ostrovsky equation. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 731-753. doi: 10.3934/dcds.2004.10.731 |
[14] |
Adrien Dekkers, Anna Rozanova-Pierrat. Cauchy problem for the Kuznetsov equation. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 277-307. doi: 10.3934/dcds.2019012 |
[15] |
Evelyne Miot, Mario Pulvirenti, Chiara Saffirio. On the Kac model for the Landau equation. Kinetic and Related Models, 2011, 4 (1) : 333-344. doi: 10.3934/krm.2011.4.333 |
[16] |
Zheng-an Yao, Yu-Long Zhou. High order approximation for the Boltzmann equation without angular cutoff under moderately soft potentials. Kinetic and Related Models, 2020, 13 (3) : 435-478. doi: 10.3934/krm.2020015 |
[17] |
Nicolas Fournier. A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff. Kinetic and Related Models, 2019, 12 (3) : 483-505. doi: 10.3934/krm.2019020 |
[18] |
Rudong Zheng, Zhaoyang Yin. The Cauchy problem for a generalized Novikov equation. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3503-3519. doi: 10.3934/dcds.2017149 |
[19] |
Kevin Zumbrun. L∞ resolvent bounds for steady Boltzmann's Equation. Kinetic and Related Models, 2017, 10 (4) : 1255-1257. doi: 10.3934/krm.2017048 |
[20] |
Laurent Desvillettes, Clément Mouhot, Cédric Villani. Celebrating Cercignani's conjecture for the Boltzmann equation. Kinetic and Related Models, 2011, 4 (1) : 277-294. doi: 10.3934/krm.2011.4.277 |
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