The Experts below are selected from a list of 13812 Experts worldwide ranked by ideXlab platform
Jack Schaeffer - One of the best experts on this subject based on the ideXlab platform.
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a Regularity Theorem for solutions of the spherically symmetric vlasov einstein system
Communications in Mathematical Physics, 1995Co-Authors: Gerhard Rein, Alan D Rendall, Jack SchaefferAbstract:We show that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.
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a Regularity Theorem for solutions of the spherically symmetric vlasov einstein system
arXiv: General Relativity and Quantum Cosmology, 1993Co-Authors: Gerhard Rein, Alan D Rendall, Jack SchaefferAbstract:In a previous paper two of the authors (G. R. and A. D. R.) showed that there exist global, classical solutions of the spherically symmetric Vlasov-Einstein system for small initial data. The present paper continues this investigation and allows also large initial data. It is shown that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The result adds weight to the conjecture that cosmic censorship holds if one replaces dust as matter model for which naked singularities do form by a collisionless gas described by the Vlasov equation. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.
Gerhard Rein - One of the best experts on this subject based on the ideXlab platform.
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a Regularity Theorem for solutions of the spherically symmetric vlasov einstein system
Communications in Mathematical Physics, 1995Co-Authors: Gerhard Rein, Alan D Rendall, Jack SchaefferAbstract:We show that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.
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a Regularity Theorem for solutions of the spherically symmetric vlasov einstein system
arXiv: General Relativity and Quantum Cosmology, 1993Co-Authors: Gerhard Rein, Alan D Rendall, Jack SchaefferAbstract:In a previous paper two of the authors (G. R. and A. D. R.) showed that there exist global, classical solutions of the spherically symmetric Vlasov-Einstein system for small initial data. The present paper continues this investigation and allows also large initial data. It is shown that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The result adds weight to the conjecture that cosmic censorship holds if one replaces dust as matter model for which naked singularities do form by a collisionless gas described by the Vlasov equation. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.
Alan D Rendall - One of the best experts on this subject based on the ideXlab platform.
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a Regularity Theorem for solutions of the spherically symmetric vlasov einstein system
Communications in Mathematical Physics, 1995Co-Authors: Gerhard Rein, Alan D Rendall, Jack SchaefferAbstract:We show that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.
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a Regularity Theorem for solutions of the spherically symmetric vlasov einstein system
arXiv: General Relativity and Quantum Cosmology, 1993Co-Authors: Gerhard Rein, Alan D Rendall, Jack SchaefferAbstract:In a previous paper two of the authors (G. R. and A. D. R.) showed that there exist global, classical solutions of the spherically symmetric Vlasov-Einstein system for small initial data. The present paper continues this investigation and allows also large initial data. It is shown that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The result adds weight to the conjecture that cosmic censorship holds if one replaces dust as matter model for which naked singularities do form by a collisionless gas described by the Vlasov equation. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.
Senjo Shimizu - One of the best experts on this subject based on the ideXlab platform.
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strong solutions of the navier stokes equations based on the maximal lorentz Regularity Theorem in besov spaces
Journal of Functional Analysis, 2019Co-Authors: Hideo Kozono, Senjo ShimizuAbstract:Abstract We show existence and uniqueness Theorem of local strong solutions to the Navier–Stokes equations with arbitrary initial data and external forces in the homogeneous Besov space with both negative and positive differential orders which is an invariant space under the change of scaling. If the initial data and external forces are small, then the local solutions can be extended globally in time. Our solutions also belong to the Serrin class in the usual Lebesgue space. The method is based on the maximal Lorentz Regularity Theorem of the Stokes equations in the homogeneous Besov spaces. As an application, we may handle such singular data as the Dirac measure and the single layer potential supported on the sphere.
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Strong solutions of the Navier–Stokes equations based on the maximal Lorentz Regularity Theorem in Besov spaces
Journal of Functional Analysis, 2019Co-Authors: Hideo Kozono, Senjo ShimizuAbstract:Abstract We show existence and uniqueness Theorem of local strong solutions to the Navier–Stokes equations with arbitrary initial data and external forces in the homogeneous Besov space with both negative and positive differential orders which is an invariant space under the change of scaling. If the initial data and external forces are small, then the local solutions can be extended globally in time. Our solutions also belong to the Serrin class in the usual Lebesgue space. The method is based on the maximal Lorentz Regularity Theorem of the Stokes equations in the homogeneous Besov spaces. As an application, we may handle such singular data as the Dirac measure and the single layer potential supported on the sphere.
Hideo Kozono - One of the best experts on this subject based on the ideXlab platform.
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strong solutions of the navier stokes equations based on the maximal lorentz Regularity Theorem in besov spaces
Journal of Functional Analysis, 2019Co-Authors: Hideo Kozono, Senjo ShimizuAbstract:Abstract We show existence and uniqueness Theorem of local strong solutions to the Navier–Stokes equations with arbitrary initial data and external forces in the homogeneous Besov space with both negative and positive differential orders which is an invariant space under the change of scaling. If the initial data and external forces are small, then the local solutions can be extended globally in time. Our solutions also belong to the Serrin class in the usual Lebesgue space. The method is based on the maximal Lorentz Regularity Theorem of the Stokes equations in the homogeneous Besov spaces. As an application, we may handle such singular data as the Dirac measure and the single layer potential supported on the sphere.
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Strong solutions of the Navier–Stokes equations based on the maximal Lorentz Regularity Theorem in Besov spaces
Journal of Functional Analysis, 2019Co-Authors: Hideo Kozono, Senjo ShimizuAbstract:Abstract We show existence and uniqueness Theorem of local strong solutions to the Navier–Stokes equations with arbitrary initial data and external forces in the homogeneous Besov space with both negative and positive differential orders which is an invariant space under the change of scaling. If the initial data and external forces are small, then the local solutions can be extended globally in time. Our solutions also belong to the Serrin class in the usual Lebesgue space. The method is based on the maximal Lorentz Regularity Theorem of the Stokes equations in the homogeneous Besov spaces. As an application, we may handle such singular data as the Dirac measure and the single layer potential supported on the sphere.