### 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 language | English |
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Pages (from-to) | 363-418 |

Number of pages | 56 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 221 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2016 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering

### Cite this

*Archive for Rational Mechanics and Analysis*,

*221*(1), 363-418. https://doi.org/10.1007/s00205-015-0963-x

}

*Archive for Rational Mechanics and Analysis*, vol. 221, no. 1, pp. 363-418. https://doi.org/10.1007/s00205-015-0963-x

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation

AU - Carrapatoso, Kleber

AU - Tristani, Isabelle

AU - Wu, Kung Chien

PY - 2016/7/1

Y1 - 2016/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84955308826&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955308826&partnerID=8YFLogxK

U2 - 10.1007/s00205-015-0963-x

DO - 10.1007/s00205-015-0963-x

M3 - Article

AN - SCOPUS:84955308826

VL - 221

SP - 363

EP - 418

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 1

ER -