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Global solutions to the VlasovPoissonLandau system. Preprint 2011. See also arXiv:1112.3261
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Golobal solution and time decay of the VlasovPoissonLandau System in R3 x
 SIAM J. Math. Anal
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The VlasovPoissonBoltzmann system without angular cutoff, preprint 2012
"... Abstract. This paper is concerned with the VlasovPoissonBoltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angular noncutoff with −3 < γ < −2s and 1/2 ≤ s < 1, where γ, s are two parameters describing the kineti ..."
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Cited by 4 (3 self)
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Abstract. This paper is concerned with the VlasovPoissonBoltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angular noncutoff with −3 < γ < −2s and 1/2 ≤ s < 1, where γ, s are two parameters describing the kinetic and angular singularities, respectively. We establish the global existence and convergence rates of classical solutions to the Cauchy problem when initial data is near Maxwellians. This extends the results in [10, 11] for the cutoff kernel with −2 ≤ γ ≤ 1 to the case −3 < γ < −2 as long as the angular singularity exists instead and is strong enough, i.e., s is close to 1. The proof is based on the timeweighted energy method building also upon the recent studies of the non cutoff Boltzmann equation in [13] and the
GLOBAL SMOOTH DYNAMICS OF A FULLY IONIZED PLASMA WITH LONGRANGE COLLISIONS
"... Abstract. The motion of a fully ionized plasma of electrons and ions is generally governed by the VlasovMaxwellLandau system. We prove the global existence of solutions near Maxwellians to the Cauchy problem of the system for the longrange collision kernel of soft potentials, particularly inclu ..."
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Cited by 3 (0 self)
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Abstract. The motion of a fully ionized plasma of electrons and ions is generally governed by the VlasovMaxwellLandau system. We prove the global existence of solutions near Maxwellians to the Cauchy problem of the system for the longrange collision kernel of soft potentials, particularly including the classical Coulomb collision, provided that initial data is smooth enough and decays in velocity variable fast enough. As a byproduct, the convergence rates of solutions are also obtained. The proof is based on the energy method through designing a new temporal energy norm to capture different features of this complex system such as dispersion of the macro component in R3, singularity of the longrange collisions and regularityloss of the electromagnetic field. 1.
The VlasovPoissonBoltzmann system for the whole range of cutoff soft potentials
, 2014
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STABILITY OF THE NONRELATIVISTIC VLASOVMAXWELLBOLTZMANN SYSTEM FOR ANGULAR NONCUTOFF POTENTIALS
"... Abstract. Although there recently have been extensive studies on the perturbation theory of the angular noncutoff Boltzmann equation (cf. [4] and [17]), it remains mathematically unknown when there is a selfconsistent Lorentz force coupled with the Maxwell equations in the nonrelativistic approxi ..."
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Cited by 2 (2 self)
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Abstract. Although there recently have been extensive studies on the perturbation theory of the angular noncutoff Boltzmann equation (cf. [4] and [17]), it remains mathematically unknown when there is a selfconsistent Lorentz force coupled with the Maxwell equations in the nonrelativistic approximation. In the paper, for perturbative initial data with suitable regularity and integrability, we establish the large time stability of solutions to the Cauchy problem on the VlasovMaxwellBoltzmann system with physical angular noncutoff intermolecular collisions including the inverse power law potentials, and also obtain as a byproduct the convergence rates of solutions. The proof is based on a refined timevelocity weighted energy method with two key technical parts: one is to introduce the exponentially weighted estimates into the noncutoff Boltzmann operator and the other to design a delicate temporal energy X(t)norm to obtain its uniform bound. The result also extends the case of the hard sphere model considered by Guo (Invent. Math. 153(3): 593–630 (2003)) to the general collision potentials.
Negative Sobolev Spaces and the Twospecies VlasovMaxwellLandau System in the Whole Space
"... A global solvability result of the Cauchy problem of the twospecies VlasovMaxwellLandau system near a given global Maxwellian is established by employing an approach different than that of [5]. Compared with that of [5], the minimal regularity index and the smallness assumptions we imposed on the ..."
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A global solvability result of the Cauchy problem of the twospecies VlasovMaxwellLandau system near a given global Maxwellian is established by employing an approach different than that of [5]. Compared with that of [5], the minimal regularity index and the smallness assumptions we imposed on the initial data are weaker. Our analysis does not rely on the decay of the corresponding linearized system and the Duhamel principle and thus it can be used to treat the onespecies VlasovMaxwellLandau system for the case of γ> −3 and the onespecies VlasovMaxwellBoltzmann system for the case of −1 < γ ≤ 1 to deduce the global existence results together with the corresponding temporal decay estimates. 1 Introduction and main results The motion of a fully ionized plasma consisting of only two species particles (e.g. electrons and ions) under the influence of the selfconsistent Lorentz force and binary collisions is governed by the following twospecies
THE VLASOVPOISSONLANDAU SYSTEM IN R 3 x
, 1202
"... Abstract. For the LandauPoisson system with Coulomb interaction in R 3 x, we prove the global existence, uniqueness, and large time convergence rates to the Maxwellian equilibrium for solutions which start out sufficiently close. Contents ..."
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Abstract. For the LandauPoisson system with Coulomb interaction in R 3 x, we prove the global existence, uniqueness, and large time convergence rates to the Maxwellian equilibrium for solutions which start out sufficiently close. Contents