Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.13538 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915623152386048 |
|---|---|
| author | Manatova, Nailya |
| author_facet | Manatova, Nailya |
| contents | For the quintic, mass critical generalized Korteweg-de Vries equation, for any $ν\in (\frac{1}{2}, 1)$, we prove the existence of solutions in the energy space that blow up in finite time $T>0$ with the blow-up rate $\|\partial_x u(t)\|_{L^2} \sim (T-t)^{-ν}$ (infinite point blow-up). These solutions are constructed arbitrarily close to the family of solitons and correspond to the concentration of a soliton traveling at $+\infty$ in space as $t\uparrow T$. This complements the previous results obtained in the work of Martel, Merle, Raphaël in 2015 on infinite point exotic blow-up, which were valid under the technical restriction $ν>\frac {11}{13}$. The value $ν=\frac 12$ corresponds to a critical case to be treated elsewhere. At the technical level, we implement a modification of the virial-energy functional, to allow all $ν> \frac 12$ and simplify the proof of energy estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Full range of infinite point blow-up exponents for the critical generalized KdV equation Manatova, Nailya Analysis of PDEs For the quintic, mass critical generalized Korteweg-de Vries equation, for any $ν\in (\frac{1}{2}, 1)$, we prove the existence of solutions in the energy space that blow up in finite time $T>0$ with the blow-up rate $\|\partial_x u(t)\|_{L^2} \sim (T-t)^{-ν}$ (infinite point blow-up). These solutions are constructed arbitrarily close to the family of solitons and correspond to the concentration of a soliton traveling at $+\infty$ in space as $t\uparrow T$. This complements the previous results obtained in the work of Martel, Merle, Raphaël in 2015 on infinite point exotic blow-up, which were valid under the technical restriction $ν>\frac {11}{13}$. The value $ν=\frac 12$ corresponds to a critical case to be treated elsewhere. At the technical level, we implement a modification of the virial-energy functional, to allow all $ν> \frac 12$ and simplify the proof of energy estimates. |
| title | Full range of infinite point blow-up exponents for the critical generalized KdV equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.13538 |