تقرير
On the convergence rates of discrete solutions to the Wave Kinetic Equation
| العنوان: | On the convergence rates of discrete solutions to the Wave Kinetic Equation |
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| المؤلفون: | Dolce, Michele, Grande, Ricardo |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematical Physics, 35B40, 45G05, 35Q55 |
| الوصف: | In this paper, we consider the long-term behavior of some special solutions to the Wave Kinetic Equation (WKE). This equation provides a mesoscopic description of wave systems interacting nonlinearly via the cubic NLS equation. Escobedo and Vel\'azquez showed that, starting with initial data given by countably many Dirac masses, solutions remain a linear combination of countably many Dirac masses at all times. Moreover, there is convergence to a single Dirac mass at long times. The first goal of this paper is to give quantitative rates for the speed of said convergence. In order to study the optimality of the bounds we obtain, we introduce and analyze a toy model accounting only for the leading order quadratic interactions. Comment: 19 pages, comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.14400 |
| رقم الأكسشن: | edsarx.2404.14400 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |