Gevrey regularity for solution of the spatially homogeneous landau equation
نویسندگان
چکیده
منابع مشابه
Gevrey Regularity for the Solution of the Spatially Homogeneous Landau Equation
This is a non-linear diffusion equation, and the coefficients āi j, c̄ depend on the solution f . Here we are mainly concerned with the Gevrey class regularity for the solution of the Landau equation. This equation is obtained as a limit of the Boltzmann equation when the collisions become grazing (see [8] and references therein). Recently, a lot of progress has been made on the study of the Sob...
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There are many papers concerning the propagation of regularity for the solution of the Boltzmann equation (cf. [5, 6, 8, 9, 13] and references therein). In these works, it has been shown that the Sobolev or Lebesgue regularity satisfied by the initial datum is propagated along the time variable. The solutions having the Gevrey regularity for a finite time have been constructed in [15] in which ...
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Abstract. We consider the spatially homogeneous Landau equation of kinetic theory, and provide a differential inequality for the Wasserstein distance with quadratic cost between two solutions. We deduce some well-posedness results. The main difficulty is that this equation presents a singularity for small relative velocities. Our uniqueness result is the first one in the important case of soft ...
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Abstract. We consider the spatially homogeneous Landau equation of kinetic theory, and provide a differential inequality for the Wasserstein distance with quadratic cost between two solutions. We deduce some well-posedness results. The main difficulty is that this equation presents a singularity for small relative velocities. Our uniqueness result is the first one in the important case of soft ...
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We nd a lower bound for the entropy dissipation of the spatially homogeneous Landau equation with hard potentials in terms of the entropy itself. We deduce from this explicit estimates on the speed of convergence towards equilibrium for the solution of this equation. In the case of so-called overmaxwellian potentials, the convergence is exponential. We also compute a lower bound for the spectra...
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ژورنال
عنوان ژورنال: Acta Mathematica Scientia
سال: 2009
ISSN: 0252-9602
DOI: 10.1016/s0252-9602(09)60063-1