Published May 2020
| Submitted
Journal Article
Open
Singularity formation and global Well-posedness for the generalized Constantin–Lax–Majda equation with dissipation
- Creators
- Chen, Jiajie
Abstract
We study a generalization due to De Gregorio and Wunsch et al of the Constantin–Lax–Majda equation (gCLM) on the real line ω_t + auω_x = u_xω−νΛ^γω, u_x = Hω, where H is the Hilbert transform and Λ=(−∂_(xx))^(1/2) . We use the method in Chen J et al (2019 (arXiv:1905.06387)) to prove finite time self-similar blowup for a close to 1/2 and γ=2 by establishing nonlinear stability of an approximate self-similar profile. For a > −1, we discuss several classes of initial data and establish global well-posedness and an one-point blowup criterion for different initial data. For a ≤ -1, we prove global well-posedness for gCLM with critical and supercritical dissipation.
Additional Information
© 2020 IOP Publishing Ltd & London Mathematical Society. Received 28 August 2019; Accepted 10 February 2020; Published 23 March 2020.Attached Files
Submitted - 1908.09385.pdf
Files
1908.09385.pdf
Files
(355.6 kB)
Name | Size | Download all |
---|---|---|
md5:a2056a4acbe2110acdc3632d431fcf1b
|
355.6 kB | Preview Download |
Additional details
- Eprint ID
- 102098
- Resolver ID
- CaltechAUTHORS:20200325-070208161
- DMS-1907977
- NSF
- Created
-
2020-03-25Created from EPrint's datestamp field
- Updated
-
2022-07-12Created from EPrint's last_modified field