TY - JOUR

T1 - Erratum to

T2 - Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation (Archive for Rational Mechanics and Analysis, (2016), 221, 1, (363-418), 10.1007/s00205-015-0963-x)

AU - Carrapatoso, Kleber

AU - Tristani, Isabelle

AU - Wu, Kung Chien

N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - We correct a mistake in “Cauchy problem and exponential stability for the inhomogeneous Landau equation”, Arch. Rational Mech. Anal. 221, 1 (2016), 363-418. In the study of the linearized equation in Section 2, estimate (2.27) in Lemma 2.8 is not correct, and this error is then straithgforwardly propagated to (2.5) in Theorem 2.3 and to the second estimate in Corollary 3.1. This last estimate is then used to treat the nonlinear equation in the proof of Proposition 3.7. In this erratum we first show another (weaker) regularity estimate in the place of (2.27), which is then propagated to Theorem 2.3 and Corollary 3.1. Finally we show how the last estimate is used in the proof of Proposition 3.7. The results of the original paper remain unchanged, and the new regularity estimate we shall prove here is a direct consequence of the techniques already presented in the paper. The only modification to perform is in the condition (H0)-(i) that need to be changed into k > 3γ/2 + 7 + 3/2. Remark. Estimates (2.20) and (2.21) are not correct either, and they could also be replaced. However we do not deal with them here since they are not used to treat the nonlinear equation.

AB - We correct a mistake in “Cauchy problem and exponential stability for the inhomogeneous Landau equation”, Arch. Rational Mech. Anal. 221, 1 (2016), 363-418. In the study of the linearized equation in Section 2, estimate (2.27) in Lemma 2.8 is not correct, and this error is then straithgforwardly propagated to (2.5) in Theorem 2.3 and to the second estimate in Corollary 3.1. This last estimate is then used to treat the nonlinear equation in the proof of Proposition 3.7. In this erratum we first show another (weaker) regularity estimate in the place of (2.27), which is then propagated to Theorem 2.3 and Corollary 3.1. Finally we show how the last estimate is used in the proof of Proposition 3.7. The results of the original paper remain unchanged, and the new regularity estimate we shall prove here is a direct consequence of the techniques already presented in the paper. The only modification to perform is in the condition (H0)-(i) that need to be changed into k > 3γ/2 + 7 + 3/2. Remark. Estimates (2.20) and (2.21) are not correct either, and they could also be replaced. However we do not deal with them here since they are not used to treat the nonlinear equation.

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U2 - 10.1007/s00205-016-1064-1

DO - 10.1007/s00205-016-1064-1

M3 - Comment/debate

AN - SCOPUS:84997285777

VL - 223

SP - 1035

EP - 1037

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -