TY - JOUR
T1 - Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation
AU - Carrapatoso, Kleber
AU - Tristani, Isabelle
AU - Wu, Kung Chien
N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
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.
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U2 - 10.1007/s00205-015-0963-x
DO - 10.1007/s00205-015-0963-x
M3 - Article
AN - SCOPUS:84955308826
SN - 0003-9527
VL - 221
SP - 363
EP - 418
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 1
ER -