In this expository note we review some recent results on Landau damping in the nonlinear Vlasov equations, focusing specifically on the recent construction of nonlinear echo solutions by the author [arXiv:1605.06841] and the associated background. These solutions show that a straightforward extension of Mouhot and Villani’s theorem on Landau damping to Sobolev spaces on is impossible and hence emphasize the subtle dependence on regularity of phase mixing problems. This expository note is specifically aimed at mathematicians who study the analysis of PDEs, but not necessarily those who work specifically on kinetic theory. However, for the sake of brevity, this review is certainly not comprehensive.
@article{JEDP_2017____A2_0, author = {Bedrossian, Jacob}, title = {A brief summary of nonlinear echoes and {Landau} damping}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, note = {talk:2}, pages = {1--14}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2017}, doi = {10.5802/jedp.652}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.652/} }
TY - JOUR AU - Bedrossian, Jacob TI - A brief summary of nonlinear echoes and Landau damping JO - Journées équations aux dérivées partielles N1 - talk:2 PY - 2017 SP - 1 EP - 14 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.652/ DO - 10.5802/jedp.652 LA - en ID - JEDP_2017____A2_0 ER -
%0 Journal Article %A Bedrossian, Jacob %T A brief summary of nonlinear echoes and Landau damping %J Journées équations aux dérivées partielles %Z talk:2 %D 2017 %P 1-14 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.652/ %R 10.5802/jedp.652 %G en %F JEDP_2017____A2_0
Bedrossian, Jacob. A brief summary of nonlinear echoes and Landau damping. Journées équations aux dérivées partielles (2017), Talk no. 2, 14 p. doi : 10.5802/jedp.652. http://www.numdam.org/articles/10.5802/jedp.652/
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