|
|||||
 |
|
|
|
|
|
|
|
On the propagation of
regularity for solutions of the dispersion generalized
Benjamin–Ono equation
Argenis J. Mendez |
|
Vol. 13 (2020), No. 8, 2399–2440
|
Abstract |
|
We study some properties of propagation of regularity of solutions of the dispersive generalized Benjamin–Ono (BO) equation. This model defines a family of dispersive equations that can be seen as a dispersive interpolation between the Benjamin–Ono equation and the Korteweg–de Vries (KdV) equation. Recently, it has been shown that solutions of the KdV and BO equations satisfy the following property: if the initial data has some prescribed regularity on the right-hand side of the real line, then this regularity is propagated with infinite speed by the flow solution. In this case the nonlocal term present in the dispersive generalized Benjamin–Ono equation is more challenging that the one in the BO equation. To deal with this a new approach is needed. The new ingredient is to combine commutator expansions into the weighted energy estimate. This allows us to obtain the property of propagation and explicitly the smoothing effect. |
|
To my parents |
PDF Access Denied
We have not been able to recognize your IP address
18.189.178.34
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
dispersive generalized Benjamin–Ono equation,
well-posedness, propagation of regularity, refined
Strichartz
|
Mathematical Subject Classification 2010
Primary: 35Q53
Secondary: 35Q05
|
Milestones
Received: 14 March 2019
Revised: 26 July 2019
Accepted: 25 September 2019
Published: 28 December 2020
|
Authors |
| Argenis J. Mendez | |
| Instituto Nacional de Matematica
Pura e Aplicada Rio de Janeiro Brasil |
|
