| Softcover ISBN: | 978-2-85629-955-5 |
| Product Code: | SMFMEM/172 |
| List Price: | $53.00 |
| AMS Member Price: | $42.40 |
| Softcover ISBN: | 978-2-85629-955-5 |
| Product Code: | SMFMEM/172 |
| List Price: | $53.00 |
| AMS Member Price: | $42.40 |
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Book DetailsMémoires de la Société Mathématique de FranceVolume: 172; 2022; 123 ppMSC: Primary 35
The author proves almost sharp decay estimates for the small data solutions and their derivatives of the Vlasov-Maxwell system in dimension \(n \ge 4\). The smallness assumption concerns only certain weighted \(L^1\) or \(L^2\) norms of the initial data. In particular, no compact support assumption is required on the Vlasov or the Maxwell fields. The main ingredients of the proof are vector field methods for both the kinetic and the wave equations, null properties of the Vlasov-Maxwell system to control high velocities and a new decay estimate for the velocity average of the solution of the relativistic massive transport equation.
The author also considers the massless Vlasov-Maxwell system under a lower bound on the velocity support of the Vlasov field. As he proves in this book, the velocity support of the Vlasov field needs to be initially bounded away from \(0\). The author compensates the weaker decay estimate on the velocity average of the massless Vlasov field near the light cone by an extra null decomposition of the velocity vector.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
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The author proves almost sharp decay estimates for the small data solutions and their derivatives of the Vlasov-Maxwell system in dimension \(n \ge 4\). The smallness assumption concerns only certain weighted \(L^1\) or \(L^2\) norms of the initial data. In particular, no compact support assumption is required on the Vlasov or the Maxwell fields. The main ingredients of the proof are vector field methods for both the kinetic and the wave equations, null properties of the Vlasov-Maxwell system to control high velocities and a new decay estimate for the velocity average of the solution of the relativistic massive transport equation.
The author also considers the massless Vlasov-Maxwell system under a lower bound on the velocity support of the Vlasov field. As he proves in this book, the velocity support of the Vlasov field needs to be initially bounded away from \(0\). The author compensates the weaker decay estimate on the velocity average of the massless Vlasov field near the light cone by an extra null decomposition of the velocity vector.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
