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On Stop-and-Go waves in dense traffic
Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff
1. | Department of Mathematics, City University of Hong Kong, Hong Kong, China |
2. | Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, 606-8501, Japan |
3. | Liu Bie Ju Centre for Mathematical Sciences, City university of Hong Kong, Hong Kong, China |
4. | Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong |
[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] |
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 |
[3] |
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 |
[4] |
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 |
[5] |
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 |
[6] |
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 |
[7] |
Thomas Kappeler, Riccardo Montalto. Normal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022048 |
[8] |
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 |
[9] |
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 |
[10] |
Nadia Lekrine, Chao-Jiang Xu. Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation. Kinetic and Related Models, 2009, 2 (4) : 647-666. doi: 10.3934/krm.2009.2.647 |
[11] |
Lanzhe Liu. Mean oscillation and boundedness of Toeplitz Type operators associated to pseudo-differential operators. Communications on Pure and Applied Analysis, 2015, 14 (2) : 627-636. doi: 10.3934/cpaa.2015.14.627 |
[12] |
Liang Huang, Jiao Chen. The boundedness of multi-linear and multi-parameter pseudo-differential operators. Communications on Pure and Applied Analysis, 2021, 20 (2) : 801-815. doi: 10.3934/cpaa.2020291 |
[13] |
JIAO CHEN, WEI DAI, GUOZHEN LU. $L^p$ boundedness for maximal functions associated with multi-linear pseudo-differential operators. Communications on Pure and Applied Analysis, 2017, 16 (3) : 883-898. doi: 10.3934/cpaa.2017042 |
[14] |
Ildoo Kim. An $L_p$-Lipschitz theory for parabolic equations with time measurable pseudo-differential operators. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2751-2771. doi: 10.3934/cpaa.2018130 |
[15] |
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 |
[16] |
A. V. Bobylev, Vladimir Dorodnitsyn. Symmetries of evolution equations with non-local operators and applications to the Boltzmann equation. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : 35-57. doi: 10.3934/dcds.2009.24.35 |
[17] |
Dinh Nguyen Duy Hai. Hölder-Logarithmic type approximation for nonlinear backward parabolic equations connected with a pseudo-differential operator. Communications on Pure and Applied Analysis, 2022, 21 (5) : 1715-1734. doi: 10.3934/cpaa.2022043 |
[18] |
Yan Yong, Weiyuan Zou. Macroscopic regularity for the relativistic Boltzmann equation with initial singularities. Kinetic and Related Models, 2019, 12 (5) : 945-967. doi: 10.3934/krm.2019036 |
[19] |
Thomas Chen, Ryan Denlinger, Nataša Pavlović. Moments and regularity for a Boltzmann equation via Wigner transform. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 4979-5015. doi: 10.3934/dcds.2019204 |
[20] |
Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. Local existence with mild regularity for the Boltzmann equation. Kinetic and Related Models, 2013, 6 (4) : 1011-1041. doi: 10.3934/krm.2013.6.1011 |
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