Hydrodynamic limits of the nonlinear Schrödinger equation with the Chern-Simons gauge fields
| العنوان: | Hydrodynamic limits of the nonlinear Schrödinger equation with the Chern-Simons gauge fields |
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| المؤلفون: | Jeongho Kim, Bora Moon |
| المصدر: | Discrete and Continuous Dynamical Systems. 42:2541 |
| بيانات النشر: | American Institute of Mathematical Sciences (AIMS), 2022. |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Applied Mathematics, Discrete Mathematics and Combinatorics, Analysis |
| الوصف: | We present two types of the hydrodynamic limit of the nonlinear Schrödinger-Chern-Simons (SCS) system. We consider two different scalings of the SCS system and show that each SCS system asymptotically converges towards the compressible and incompressible Euler system, coupled with the Chern-Simons equations and Poisson equation respectively, as the scaled Planck constant converges to 0. Our method is based on the modulated energy estimate. In the case of compressible limit, we observe that the classical theory of relative entropy method can be applied to show the hydrodynamic limit, with the additional quantum correction term. On the other hand, for the incompressible limit, we directly estimate the modulated energy to derive the desired asymptotic convergence. |
| تدمد: | 1553-5231 1078-0947 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::caf5af888e9c67e9339514ecd1f3def7 https://doi.org/10.3934/dcds.2021202 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi...........caf5af888e9c67e9339514ecd1f3def7 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15535231 10780947 |
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