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A review of Boltzmann equation with singular kernels
1. | Irenav, French Naval Academy, 29240 Brest Lanveoc-Poulmic, France |
[1] |
C. David Levermore, Weiran Sun. Compactness of the gain parts of the linearized Boltzmann operator with weakly cutoff kernels. Kinetic and Related Models, 2010, 3 (2) : 335-351. doi: 10.3934/krm.2010.3.335 |
[2] |
Palle Jorgensen, James Tian. Harmonic analysis of network systems via kernels and their boundary realizations. Discrete and Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021105 |
[3] |
John R. Tucker. Attractors and kernels: Linking nonlinear PDE semigroups to harmonic analysis state-space decomposition. Conference Publications, 2001, 2001 (Special) : 366-370. doi: 10.3934/proc.2001.2001.366 |
[4] |
Radjesvarane Alexandre, Mouhamad Elsafadi. Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equations II. Non cutoff case and non Maxwellian molecules. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : 1-11. doi: 10.3934/dcds.2009.24.1 |
[5] |
Albert Erkip, Abba I. Ramadan. Existence of traveling waves for a class of nonlocal nonlinear equations with bell shaped kernels. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2125-2132. doi: 10.3934/cpaa.2017105 |
[6] |
Patricia J.Y. Wong. Existence of solutions to singular integral equations. Conference Publications, 2009, 2009 (Special) : 818-827. doi: 10.3934/proc.2009.2009.818 |
[7] |
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 |
[8] |
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 |
[9] |
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 |
[10] |
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 |
[11] |
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 |
[12] |
Xinjie Dai, Aiguo Xiao, Weiping Bu. Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler–Maruyama approximation. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021225 |
[13] |
Jifeng Chu, Zaitao Liang, Fangfang Liao, Shiping Lu. Existence and stability of periodic solutions for relativistic singular equations. Communications on Pure and Applied Analysis, 2017, 16 (2) : 591-609. doi: 10.3934/cpaa.2017029 |
[14] |
Palle E. T. Jorgensen and Steen Pedersen. Orthogonal harmonic analysis of fractal measures. Electronic Research Announcements, 1998, 4: 35-42. |
[15] |
Yong-Kum Cho. On the homogeneous Boltzmann equation with soft-potential collision kernels. Kinetic and Related Models, 2015, 8 (2) : 309-333. doi: 10.3934/krm.2015.8.309 |
[16] |
Changbing Hu, Roger Temam, Mohammed Ziane. The primitive equations on the large scale ocean under the small depth hypothesis. Discrete and Continuous Dynamical Systems, 2003, 9 (1) : 97-131. doi: 10.3934/dcds.2003.9.97 |
[17] |
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 |
[18] |
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 |
[19] |
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 |
[20] |
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 |
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