تقرير
On the wellposedness for periodic nonlinear Schr\'odinger equations with white noise dispersion
| العنوان: | On the wellposedness for periodic nonlinear Schr\'odinger equations with white noise dispersion |
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| المؤلفون: | Stewart, Gavin |
| المصدر: | Stoch PDE: Anal Comp (2023) |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Probability, 35R60, 35Q55 |
| الوصف: | We consider a periodic nonlinear Schr\"odinger equation with white noise dispersion and a power nonlinearity given by \begin{equation*} idu = \Delta u \circ dW_t + |u|^{p-1}u\;dt \end{equation*} By proving stochastic Strichartz estimates, we are able to prove almost sure global wellposedness of this equation with $L^2$ initial data for nonlinearities with exponent $1 < p \leq 3$. By generalizing the Fourier restriction spaces $X^{s,b}$ to the stochastic setting, we also prove that our solutions agree with the ones constructed by Chouk and Gubinelli using rough path techniques. We also consider the quintic equation ($p=5$), and show that it is analytically illposed in $L^1_\omega C_t L^2_x$. Comment: 17 pages, comments welcome |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s40072-023-00306-9 |
| URL الوصول: | http://arxiv.org/abs/2208.03391 |
| رقم الأكسشن: | edsarx.2208.03391 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s40072-023-00306-9 |
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