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## On the existence of exponentially decreasing solutions of the nonlinear Landau damping problem (2009)

Venue: | Indiana Univ. Math. J |

Citations: | 9 - 0 self |

### Citations

1517 |
V.I.: Mathematical methods of Classical Mechanics
- Arnold
- 1978
(Show Context)
Citation Context ...able analyticity assumptions on f∞ that will be made precise later. The decay to zero of the density for the free streaming problem, due to the dispersion of the velocities, is a well known fact (cf. =-=[2]-=-). The argument in this paper indicates that this convergence to zero plays a crucial role in the Landau damping problem. However, the averaging property is not the only ground explaining Landau dampi... |

150 |
The Cauchy Problem in Kinetic Theory
- Glassey
- 1996
(Show Context)
Citation Context ...entially fast. The mathematical theory of the Vlasov-Poisson equation, including global existence results for general initial data in space dimension N ≤ 3 has been established in several papers (cf. =-=[5]-=-, [9], [10]). Landau damping has been also extensively studied in the mathematical and physical literature (cf. [3], [4], [6], [7], [11], [12]). All the results in these papers hold only for the linea... |

129 |
Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
- Pfaffelmoser
- 1992
(Show Context)
Citation Context ...ast. The mathematical theory of the Vlasov-Poisson equation, including global existence results for general initial data in space dimension N ≤ 3 has been established in several papers (cf. [5], [9], =-=[10]-=-). Landau damping has been also extensively studied in the mathematical and physical literature (cf. [3], [4], [6], [7], [11], [12]). All the results in these papers hold only for the linearized versi... |

112 | Global existence of smooth solutions to the vlasov poisson system in three dimensions. Communications in partial differential equations - Schaeffer - 1991 |

62 | On the vibration of the electronic plasma - Landau - 1946 |

46 |
W.: Instability of periodic BGK equilibria
- Guo, Strauss
- 1995
(Show Context)
Citation Context ... data in space dimension N ≤ 3 has been established in several papers (cf. [5], [9], [10]). Landau damping has been also extensively studied in the mathematical and physical literature (cf. [3], [4], =-=[6]-=-, [7], [11], [12]). All the results in these papers hold only for the linearized version of the problem. The derivation of the exponential decay for the linearized Vlasov-Poisson system, in the cases ... |

22 |
On the kinetic theory of an assembly of particles with collective interaction
- Vlasov
- 1945
(Show Context)
Citation Context ...asov-Poisson problem, in particular the proof of Theorem 1. 2 The classical Landau linearized problem. In this Section we describe the linearized problem that was originally considered by Vlasov (cf. =-=[14]-=-) and Landau (cf. [8]) and that has been studied also in the mathematical and physical literature with different levels of rigor [3], [4], [7], [11], [12]). The goal is to explain shortly the kind of ... |

17 |
Spectral theory of the linearized Vlasov-Poisson equation
- Degond
- 1986
(Show Context)
Citation Context ...tial data in space dimension N ≤ 3 has been established in several papers (cf. [6], [10], [11]). Landau damping has been also extensively studied in the mathematical and physical literature (cf. [3], =-=[5]-=-, [7], [8], [12], [13]). The results in these papers hold only for the linearized version of the problem. The derivation of the exponential decay for the linearized Vlasov-Poisson system, in the cases... |

15 | Time asymptotics for solutions of Vlasov-Poisson equation in a circle - Caglioti, Maffei - 1998 |

12 |
The Proteins, Third Edition
- Neurath, Hill
- 1975
(Show Context)
Citation Context ...extended analytically to the domain {Im(η) > −A} for any n = ±1, ±2, .... It is worth mentioning that the function Φ (η; n) is discontinuous for η ∈ R. Indeed, due to the Plemej-Sokolski formula (cf. =-=[1]-=-): Φ (η 0 + i0) − Φ (η 0 − i0) = 2πife,v (η 0) Therefore the analytic continuation of the function Φ to the domain {Im(η) > −A} is not given by the integral formula (5.7). This is a well known propert... |

11 | Time decay for solutions to the linearized vlasov equation - Glassey, Schaeffer - 1994 |

9 |
Theory of plasma oscillations A: Origins of medium-like behavior
- BOHM, GROSS
- 1949
(Show Context)
Citation Context ...al initial data in space dimension N ≤ 3 has been established in several papers (cf. [5], [9], [10]). Landau damping has been also extensively studied in the mathematical and physical literature (cf. =-=[3]-=-, [4], [6], [7], [11], [12]). All the results in these papers hold only for the linearized version of the problem. The derivation of the exponential decay for the linearized Vlasov-Poisson system, in ... |

9 |
Longitudinal plasma oscillations
- Jackson
- 1960
(Show Context)
Citation Context ... in space dimension N ≤ 3 has been established in several papers (cf. [5], [9], [10]). Landau damping has been also extensively studied in the mathematical and physical literature (cf. [3], [4], [6], =-=[7]-=-, [11], [12]). All the results in these papers hold only for the linearized version of the problem. The derivation of the exponential decay for the linearized Vlasov-Poisson system, in the cases where... |

4 |
Propagation of moments and regularity of solutions for the 3 dimensional Vlasov-Poisson system
- Lions, Perthame
- 1991
(Show Context)
Citation Context ...lly fast. The mathematical theory of the Vlasov-Poisson equation, including global existence results for general initial data in space dimension N ≤ 3 has been established in several papers (cf. [5], =-=[9]-=-, [10]). Landau damping has been also extensively studied in the mathematical and physical literature (cf. [3], [4], [6], [7], [11], [12]). All the results in these papers hold only for the linearized... |

1 |
Long-time behaviour of the electric potential and stability in the linearized Vlasov theory
- Saenz
- 1965
(Show Context)
Citation Context ...pace dimension N ≤ 3 has been established in several papers (cf. [5], [9], [10]). Landau damping has been also extensively studied in the mathematical and physical literature (cf. [3], [4], [6], [7], =-=[11]-=-, [12]). All the results in these papers hold only for the linearized version of the problem. The derivation of the exponential decay for the linearized Vlasov-Poisson system, in the cases where such ... |