On stability of self-similar blowup for mass supercritical NLS
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929647171665920 |
|---|---|
| author | Li, Zexing |
| author_facet | Li, Zexing |
| contents | We consider the mass supercritical (NLS) in dimension $d\ge 1$ in the mass-supercritical range. The existence of self-similar blow up dyamics is known [Merle-Raphaël-Szeftel, 2010], and suitable self-similar blow up profiles were constructed [Bahri-Martel-Raphaël, 2021]. In this work, we prove the finite codimensional nonlinear asymptotic stability of a large class of self-similar profiles. The heart of the proof is, following the approach of Beceanu [Beceanu, 2011], the derivation of Strichartz dispersive estimates for matrix operators with a deformed Laplacian $Δ_b = Δ+ ib\left(\frac d2 + x\cdot\nabla\right)$ in homogeneous Sobolev spaces and energy space $H^1$. The deformed Laplacian $Δ_b$ arises from the renormalization and its operator group $e^{itΔ_b}$ exhibits self-similar dispersion, which not only recovers the free Strichartz but also enables an extension of resolvent families. Compared with Strichartz estimates based on $Δ$, this one has a larger admissible region, works for arbitrarily small polynomial decaying potential, and requires no spectral assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02078 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On stability of self-similar blowup for mass supercritical NLS Li, Zexing Analysis of PDEs 35Q55 We consider the mass supercritical (NLS) in dimension $d\ge 1$ in the mass-supercritical range. The existence of self-similar blow up dyamics is known [Merle-Raphaël-Szeftel, 2010], and suitable self-similar blow up profiles were constructed [Bahri-Martel-Raphaël, 2021]. In this work, we prove the finite codimensional nonlinear asymptotic stability of a large class of self-similar profiles. The heart of the proof is, following the approach of Beceanu [Beceanu, 2011], the derivation of Strichartz dispersive estimates for matrix operators with a deformed Laplacian $Δ_b = Δ+ ib\left(\frac d2 + x\cdot\nabla\right)$ in homogeneous Sobolev spaces and energy space $H^1$. The deformed Laplacian $Δ_b$ arises from the renormalization and its operator group $e^{itΔ_b}$ exhibits self-similar dispersion, which not only recovers the free Strichartz but also enables an extension of resolvent families. Compared with Strichartz estimates based on $Δ$, this one has a larger admissible region, works for arbitrarily small polynomial decaying potential, and requires no spectral assumption. |
| title | On stability of self-similar blowup for mass supercritical NLS |
| topic | Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2304.02078 |