| Autor: |
Ehrnström, Mats, Pei, Long |
| Rok vydání: |
2017 |
| Předmět: |
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| Zdroj: |
Journal of Evolution Equations 2018 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00028-018-0435-5 |
| Popis: |
For both localized and periodic initial data, we prove local existence in classical energy space $H^s, s>\frac{3}{2}$, for a class of dispersive equations $u_{t}+(n(u))_{x}+Lu_{x}=0$ with nonlinearities of mild regularity. Our results are valid for symmetric Fourier multiplier operators $L$ whose symbol is of temperate growth, and $n(\cdot)$ in local Sobolev space $H^{s+2}_{\mathrm{loc}}(\mathbb{R})$. In particular, the results include non-smooth and exponentially growing nonlinearities. Our proof is based on a combination of semi-group methods and a new composition result for Besov spaces. In particular, we extend a previous result for Nemytskii operators on Besov spaces on $\mathbb{R}$ to the periodic setting by using the difference-derivative characterization of Besov spaces. |
| Databáze: |
arXiv |
| Externí odkaz: |
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