Vol. 15, No. 1, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 3, 567–890
Issue 2, 273–566
Issue 1, 1–272

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
On the global behaviors for defocusing semilinear wave equations in $\mathbb{R}^{1+2}$

Dongyi Wei and Shiwu Yang

Vol. 15 (2022), No. 1, 245–272
Abstract

We study the asymptotic decay properties for defocusing semilinear wave equations in 1+2 with pure power nonlinearity. By applying new vector fields to the null hyperplane, we derive improved time decay of the potential energy, with a consequence that the solution scatters both in the critical Sobolev space and energy space for all p > 1 + 8. Moreover, combined with Brezis–Gallouet–Wainger-type of logarithmic Sobolev embedding, we show that the solution decays pointwise with sharp rate t12 when p > 11 3 and with rate t(p1)8+𝜖 for all 1 < p 11 3 . This in particular implies that the solution scatters in energy space when p > 25 1.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde

We have not been able to recognize your IP address 3.238.125.76 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
asymptotic behavior, defocusing semilinear wave equation, energy subcritical
Mathematical Subject Classification
Primary: 35L05
Milestones
Received: 4 March 2020
Revised: 9 March 2020
Accepted: 15 September 2020
Published: 16 March 2022
Authors
Dongyi Wei
School of Mathematical Sciences
Peking University
Beijing
China
Shiwu Yang
Beijing International Center for Mathematical Research
Peking University
Beijing
China