تقرير
Global existence of finite energy weak solutions to the Quantum Navier-Stokes equations with non-trivial far-field behavior
| العنوان: | Global existence of finite energy weak solutions to the Quantum Navier-Stokes equations with non-trivial far-field behavior |
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| المؤلفون: | Antonelli, Paolo, Hientzsch, Lars Eric, Spirito, Stefano |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematical Physics, 35Q35 (Primary) 35D05, 76N10 (Secondary) |
| الوصف: | We prove global existence of finite energy weak solutions to the quantum Navier-Stokes equations in the whole space with non trivial far-field condition in dimensions d = 2,3. The vacuum regions are included in the weak formulation of the equations. Our method consists in an invading domains approach. More precisely, by using a suitable truncation argument we construct a sequence of approximate solutions. The energy and the BD entropy bounds allow for the passage to the limit in the truncated formulation leading to a finite energy weak solution. Moreover, the result is also valid in the case of compressible Navier-Stokes equations with degenerate viscosity. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.jde.2021.04.025 |
| الوصول الحر: | http://arxiv.org/abs/2001.01652Test |
| رقم الانضمام: | edsarx.2001.01652 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.jde.2021.04.025 |
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