Singular initial data and uniform global bounds for the hyper-viscous Navier-Stokes equation with periodic boundary conditions. (English) Zbl 1048.35053
The author examines a generalization of incompressible Navier-Stokes equations – hyperviscous Navier-Stokes equations – with periodic boundary conditions over a rectangular domain \(\Omega\subset\mathbb{R}^n\). For initial data in \(L^p(\Omega)\), with \(p\) satisfying some condition, the local existence and uniqueness of strong solutions is established. For the case \(p= 2\), the above condition is also sufficient to establish global existence of these unique regular solutions and uniform higher-order bounds. The proof uses energy technique, Gronwall inequality and some ideas of semigroup methods.
Reviewer: Oleg Titow (Berlin)
MSC:
| 35Q30 | Navier-Stokes equations |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
Keywords:
hyperviscosity; local existence; global existence; regularity; rectangular domain; uniqueness; Gronwall inequality; semigroup methodsReferences:
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