Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

Noutchegueme, Norbert

doi:10.1063/1.4905648

Title: Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

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Abstract

Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, wemore »« less

Authors:

Noutchegueme, Norbert ^[1]

Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon)

Publication Date:: Thu Jan 15 00:00:00 EST 2015

OSTI Identifier:: 22403086

Resource Type:: Journal Article

Journal Name:: Journal of Mathematical Physics

Additional Journal Information:: Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN EQUATION; BOLTZMANN-VLASOV EQUATION; COSMOLOGICAL CONSTANT; COSMOLOGICAL MODELS; EINSTEIN FIELD EQUATIONS; FASTENERS; MATHEMATICAL SOLUTIONS; QUANTUM GRAVITY

Citation Formats


                    Ayissi, Raoul Domingo, E-mail: raoulayissi@yahoo.fr, and Noutchegueme, Norbert. Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant.  United States: N. p., 2015. 
        Web.  doi:10.1063/1.4905648.

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                    Ayissi, Raoul Domingo, E-mail: raoulayissi@yahoo.fr, & Noutchegueme, Norbert. Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant.  United States.  https://doi.org/10.1063/1.4905648

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                    Ayissi, Raoul Domingo, E-mail: raoulayissi@yahoo.fr, and Noutchegueme, Norbert. 2015.  
        "Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant".  United States.  https://doi.org/10.1063/1.4905648.

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@article{osti_22403086,

  title        = {Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant},

  author       = {Ayissi, Raoul Domingo, E-mail: raoulayissi@yahoo.fr and Noutchegueme, Norbert},

  abstractNote = {Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the global in time existence and uniqueness of a regular solution to the Einstein-Maxwell-Boltzmann system with the cosmological constant. We define and we use the weighted Sobolev separable spaces for the Boltzmann equation; some special spaces for the Einstein equations, then we clearly display all the proofs leading to the global existence theorems.},

  doi          = {10.1063/1.4905648},

  url          = {https://www.osti.gov/biblio/22403086},
  journal      = {Journal of Mathematical Physics},

  issn         = {0022-2488},

  number       = 1,

  volume       = 56,

  place        = {United States},

  year         = {Thu Jan 15 00:00:00 EST 2015},

  month        = {Thu Jan 15 00:00:00 EST 2015}

}

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