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Abstract
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We consider the spatially inhomogeneous Landau equation with Maxwellian and hard potentials (i.e,
with
) on the whole space
. We prove that if the
initial data
are close to
the vacuum solution
in an appropriate weighted norm then the solution
exists globally in time and the long-time behavior is governed by dispersion
coming from the transport operator. This work builds upon the author’s
earlier work on local existence of solutions to the Landau equation with hard
potentials.
Our proof uses an energy based approach and exploits the null structure
established by Luk in
Annals of PDE 5:11 (2019). To be able to close our estimates,
we have to couple the weighted energy estimates, which were established by the
author in
arXiv:1910.11866 (2019) with the null structure and devise new weighted
norms that take this into account.
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Keywords
stability of vacuum, Landau equation, collisions
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Mathematical Subject Classification
Primary: 35L70, 35Q99
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Milestones
Received: 7 June 2021
Revised: 21 May 2022
Accepted: 17 August 2022
Published: 21 February 2023
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