Academic Journal
Phase transitions in the fractional three-dimensional Navier–Stokes equations
| العنوان: | Phase transitions in the fractional three-dimensional Navier–Stokes equations |
|---|---|
| المؤلفون: | Boutros, Daniel W, Gibbon, John D |
| بيانات النشر: | IOP Publishing Nonlinearity |
| سنة النشر: | 2024 |
| المجموعة: | Apollo - University of Cambridge Repository |
| مصطلحات موضوعية: | 35B65, phase transition, energy balance, 35R11, regularity criteria, 35B60, fractional Navier–Stokes equations, 35B45, 76D99, 35Q35, 35B33, hypodissipation |
| الوصف: | Funder: Cambridge Trust; doi: http://dx.doi.org/10.13039/501100003343 ; Funder: Prince Bernhard Culture Fund ; Funder: Cantab Capital Institute for Mathematics of Information ; The fractional Navier–Stokes equations on a periodic domain [0, L]3 differ from their conventional counterpart by the replacement of the −νΔu Laplacian term by νsAsu , where A=−Δ is the Stokes operator and νs=νL2(s−1) is the viscosity parameter. Four critical values of the exponent s⩾0 have been identified where functional properties of solutions of the fractional Navier–Stokes equations change. These values are: s=13 ; s=34 ; s=56 and s=54 . In particular: (i) for s>13 we prove an analogue of one of the Prodi–Serrin regularity criteria; (ii) for s⩾34 we find an equation of local energy balance and; (iii) for s>56 we find an infinite hierarchy of weak solution time averages. The existence of our analogue of the Prodi–Serrin criterion for s>13 suggests the sharpness of the construction using convex integration of Hölder continuous solutions with epochs of regularity in the range 0 |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | text/xml; application/pdf |
| اللغة: | English |
| Relation: | https://www.repository.cam.ac.uk/handle/1810/368002 |
| الاتاحة: | https://www.repository.cam.ac.uk/handle/1810/368002 |
| رقم الانضمام: | edsbas.7FC3050A |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |