Villani C. Hypocoercivity. - Providence, R.I.: American Mathematical Society, 2009. - v, 141 p. - (Memoirs of the American Mathematical Society; Vol.202, N 950). - Bibliogr.: p.139-141. - ISBN 978-0-8218-4498-4; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Introduction .................................................... 1 Part I. L = A*A + B ........................................... 5 1 Notation ..................................................... 7 2 Operators L = A*A + B ........................................ 9 3 Coercivity and hypocoercivity ............................... 13 4 Basic theorem ............................................... 17 5 Generalization .............................................. 23 6 Hypocoercivity in entropic sense ............................ 28 7 Application: the kinetic Fokker-Planck equation ............. 40 8 The method of multipliers ................................... 46 9 Further applications and open problems ...................... 50 Part II. The auxiliary operator method ........................ 55 10 Assumptions ................................................. 57 11 Main theorem ................................................ 58 12 Simplified theorem and applications ......................... 61 13 Discussion and open problems ................................ 63 Part III. Fully nonlinear equations ............................ 65 14 Main abstract theorem ....................................... 67 15 Proof of the Main Theorem ................................... 70 16 Compressible Navier-Stokes system ........................... 80 17 Weakly self-consistent Vlasov-Fokker-Planck equation ........ 83 18 Boltzmann equation .......................................... 87 Appendices .................................................... 103 A.19 Some criteria for Poincare inequalities .................. 105 A.20 Well-posedness for the Fokker-Planck equation ............ 109 A.21 Some methods for global hypoellipticity .................. 113 A.22 Local positivity estimates ............................... 127 A.23 Toolbox .................................................. 130 Bibliography .................................................. 139