December  2008, 1(4): 491-513. doi: 10.3934/krm.2008.1.491

Integral estimates for a linear singular operator linked with Boltzmann operators part II: High singularities $1\le\nu<2$

1. 

IRENAV, French Naval Academy, 29240 BREST ARMEES, France

2. 

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received  June 2008 Revised  June 2008 Published  October 2008

In this work, we show that integral estimates for a linear operator linked with Boltzmann quadratic operator considered in [1] can also be obtained for the case of higher singularities. Some estimates proven in this earlier work are improved, as in particular, we do not need any regularity with respect to the first function.
Citation: Radjesvarane Alexandre, Lingbing He. Integral estimates for a linear singular operator linked with Boltzmann operators part II: High singularities $1\le\nu<2$. Kinetic & Related Models, 2008, 1 (4) : 491-513. doi: 10.3934/krm.2008.1.491
[1]

Robert M. Strain. Optimal time decay of the non cut-off Boltzmann equation in the whole space. Kinetic & Related Models, 2012, 5 (3) : 583-613. doi: 10.3934/krm.2012.5.583

[2]

Lvqiao Liu, Hao Wang. Global existence and decay of solutions for hard potentials to the fokker-planck-boltzmann equation without cut-off. Communications on Pure & Applied Analysis, 2020, 19 (6) : 3113-3136. doi: 10.3934/cpaa.2020135

[3]

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) : 335-351. doi: 10.3934/krm.2010.3.335

[4]

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

[5]

Radjesvarane Alexandre. A review of Boltzmann equation with singular kernels. Kinetic & Related Models, 2009, 2 (4) : 551-646. doi: 10.3934/krm.2009.2.551

[6]

Andrea Bondesan, Laurent Boudin, Marc Briant, Bérénice Grec. Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium maxwell distributions. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2549-2573. doi: 10.3934/cpaa.2020112

[7]

Ricardo J. Alonso, Irene M. Gamba. Gain of integrability for the Boltzmann collisional operator. Kinetic & Related Models, 2011, 4 (1) : 41-51. doi: 10.3934/krm.2011.4.41

[8]

Palle E. T. Jorgensen and Steen Pedersen. Orthogonal harmonic analysis of fractal measures. Electronic Research Announcements, 1998, 4: 35-42.

[9]

Yong-Kum Cho. On the homogeneous Boltzmann equation with soft-potential collision kernels. Kinetic & Related Models, 2015, 8 (2) : 309-333. doi: 10.3934/krm.2015.8.309

[10]

Cédric Villani. Regularity of optimal transport and cut locus: From nonsmooth analysis to geometry to smooth analysis. Discrete & Continuous Dynamical Systems - A, 2011, 30 (2) : 559-571. doi: 10.3934/dcds.2011.30.559

[11]

Corrado Mascia. Stability analysis for linear heat conduction with memory kernels described by Gamma functions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (8) : 3569-3584. doi: 10.3934/dcds.2015.35.3569

[12]

Yong-Kum Cho. A quadratic Fourier representation of the Boltzmann collision operator with an application to the stability problem. Kinetic & Related Models, 2012, 5 (3) : 441-458. doi: 10.3934/krm.2012.5.441

[13]

Raf Cluckers, Julia Gordon, Immanuel Halupczok. Motivic functions, integrability, and applications to harmonic analysis on $p$-adic groups. Electronic Research Announcements, 2014, 21: 137-152. doi: 10.3934/era.2014.21.137

[14]

Frédéric Robert. On the influence of the kernel of the bi-harmonic operator on fourth order equations with exponential growth. Conference Publications, 2007, 2007 (Special) : 875-882. doi: 10.3934/proc.2007.2007.875

[15]

Mark F. Demers, Hong-Kun Zhang. Spectral analysis of the transfer operator for the Lorentz gas. Journal of Modern Dynamics, 2011, 5 (4) : 665-709. doi: 10.3934/jmd.2011.5.665

[16]

G. A. Swarup. On the cut point conjecture. Electronic Research Announcements, 1996, 2: 98-100.

[17]

Yong-Kum Cho, Hera Yun. On the gain of regularity for the positive part of Boltzmann collision operator associated with soft-potentials. Kinetic & Related Models, 2012, 5 (4) : 769-786. doi: 10.3934/krm.2012.5.769

[18]

Nicolas Lerner, Yoshinori Morimoto, Karel Pravda-Starov, Chao-Jiang Xu. Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators. Kinetic & Related Models, 2013, 6 (3) : 625-648. doi: 10.3934/krm.2013.6.625

[19]

C E Yarman, B Yazıcı. A new exact inversion method for exponential Radon transform using the harmonic analysis of the Euclidean motion group. Inverse Problems & Imaging, 2007, 1 (3) : 457-479. doi: 10.3934/ipi.2007.1.457

[20]

Lijian Jiang, Craig C. Douglas. Analysis of an operator splitting method in 4D-Var. Conference Publications, 2009, 2009 (Special) : 394-403. doi: 10.3934/proc.2009.2009.394

2018 Impact Factor: 1.38

Metrics

  • PDF downloads (29)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]