Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation

Kleber Carrapatoso, Isabelle Tristani, Kung Chien Wu

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This work deals with the inhomogeneous Landau equation on the torus in the cases of hard, Maxwellian and moderately soft potentials. We first investigate the linearized equation and we prove exponential decay estimates for the associated semigroup. We then turn to the nonlinear equation and we use the linearized semigroup decay in order to construct solutions in a close-to-equilibrium setting. Finally, we prove an exponential stability for such a solution, with a rate as close as we want to the optimal rate given by the semigroup decay.

Original languageEnglish
Pages (from-to)363-418
Number of pages56
JournalArchive for Rational Mechanics and Analysis
Volume221
Issue number1
DOIs
Publication statusPublished - 2016 Jul 1

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Landau Equation
Exponential Stability
Asymptotic stability
Cauchy Problem
Semigroup
Nonlinear equations
Decay
Optimal Rates
Decay Estimates
Exponential Decay
Torus
Nonlinear Equations

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

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Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation. / Carrapatoso, Kleber; Tristani, Isabelle; Wu, Kung Chien.

In: Archive for Rational Mechanics and Analysis, Vol. 221, No. 1, 01.07.2016, p. 363-418.

Research output: Contribution to journalArticle

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