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From particle to kinetic and hydrodynamic descriptions of flocking
A new regularization possibility for the Boltzmann equation with soft potentials
1.  LAMA UMR 8050, Faculté de Sciences et Technologies, Université Paris Est, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France 
[1] 
Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, ChaoJiang Xu, Tong Yang. Uniqueness of solutions for the noncutoff Boltzmann equation with soft potential. Kinetic & Related Models, 2011, 4 (4) : 919934. doi: 10.3934/krm.2011.4.919 
[2] 
Yingzhe Fan, Yuanjie Lei. The Boltzmann equation with frictional force for very soft potentials in the whole space. Discrete & Continuous Dynamical Systems  A, 2019, 39 (7) : 43034329. doi: 10.3934/dcds.2019174 
[3] 
Nicolas Fournier. A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff. Kinetic & Related Models, 2019, 12 (3) : 483505. doi: 10.3934/krm.2019020 
[4] 
Léo Glangetas, HaoGuang Li, ChaoJiang Xu. Sharp regularity properties for the noncutoff spatially homogeneous Boltzmann equation. Kinetic & Related Models, 2016, 9 (2) : 299371. doi: 10.3934/krm.2016.9.299 
[5] 
Zhaohui Huo, Yoshinori Morimoto, Seiji Ukai, Tong Yang. Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff. Kinetic & Related Models, 2008, 1 (3) : 453489. doi: 10.3934/krm.2008.1.453 
[6] 
Yoshinori Morimoto, Seiji Ukai, ChaoJiang Xu, Tong Yang. Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff. Discrete & Continuous Dynamical Systems  A, 2009, 24 (1) : 187212. doi: 10.3934/dcds.2009.24.187 
[7] 
Lingbing He, Yulong Zhou. High order approximation for the Boltzmann equation without angular cutoff. Kinetic & Related Models, 2018, 11 (3) : 547596. doi: 10.3934/krm.2018024 
[8] 
Renjun Duan, Shuangqian Liu, Tong Yang, Huijiang Zhao. Stability of the nonrelativistic VlasovMaxwellBoltzmann system for angular noncutoff potentials. Kinetic & Related Models, 2013, 6 (1) : 159204. doi: 10.3934/krm.2013.6.159 
[9] 
Radjesvarane Alexandre, Jie Liao, Chunjin Lin. Some a priori estimates for the homogeneous Landau equation with soft potentials. Kinetic & Related Models, 2015, 8 (4) : 617650. doi: 10.3934/krm.2015.8.617 
[10] 
YongKum Cho. On the homogeneous Boltzmann equation with softpotential collision kernels. Kinetic & Related Models, 2015, 8 (2) : 309333. doi: 10.3934/krm.2015.8.309 
[11] 
YongKum Cho, Hera Yun. On the gain of regularity for the positive part of Boltzmann collision operator associated with softpotentials. Kinetic & Related Models, 2012, 5 (4) : 769786. doi: 10.3934/krm.2012.5.769 
[12] 
JeanMarie Barbaroux, Dirk Hundertmark, Tobias Ried, Semjon Vugalter. Strong smoothing for the noncutoff homogeneous Boltzmann equation for Maxwellian molecules with DebyeYukawa type interaction. Kinetic & Related Models, 2017, 10 (4) : 901924. doi: 10.3934/krm.2017036 
[13] 
Robert M. Strain, Keya Zhu. Largetime decay of the soft potential relativistic Boltzmann equation in $\mathbb{R}^3_x$. Kinetic & Related Models, 2012, 5 (2) : 383415. doi: 10.3934/krm.2012.5.383 
[14] 
Kevin Zumbrun. L^{∞} resolvent bounds for steady Boltzmann's Equation. Kinetic & Related Models, 2017, 10 (4) : 12551257. doi: 10.3934/krm.2017048 
[15] 
Laurent Desvillettes, Clément Mouhot, Cédric Villani. Celebrating Cercignani's conjecture for the Boltzmann equation. Kinetic & Related Models, 2011, 4 (1) : 277294. doi: 10.3934/krm.2011.4.277 
[16] 
Nadia Lekrine, ChaoJiang Xu. Gevrey regularizing effect of the Cauchy problem for noncutoff homogeneous Kac's equation. Kinetic & Related Models, 2009, 2 (4) : 647666. doi: 10.3934/krm.2009.2.647 
[17] 
C. David Levermore, Weiran Sun. Compactness of the gain parts of the linearized Boltzmann operator with weakly cutoff kernels. Kinetic & Related Models, 2010, 3 (2) : 335351. doi: 10.3934/krm.2010.3.335 
[18] 
Shaofei Wu, Mingqing Wang, Maozhu Jin, Yuntao Zou, Lijun Song. Uniform $L^1$ stability of the inelastic Boltzmann equation with large external force for hard potentials. Discrete & Continuous Dynamical Systems  S, 2019, 12 (4&5) : 10051013. doi: 10.3934/dcdss.2019068 
[19] 
Bernd Hofmann, Barbara Kaltenbacher, Elena Resmerita. Lavrentiev's regularization method in Hilbert spaces revisited. Inverse Problems & Imaging, 2016, 10 (3) : 741764. doi: 10.3934/ipi.2016019 
[20] 
TaiPing Liu, ShihHsien Yu. Boltzmann equation, boundary effects. Discrete & Continuous Dynamical Systems  A, 2009, 24 (1) : 145157. doi: 10.3934/dcds.2009.24.145 
2018 Impact Factor: 1.38
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