Abstract
Consider a smooth bounded domain Ω ⊆ ℝ3 with boundary ∂Ω, a time interval [0, T), 0<T ≤ ∞, and the Navier-Stokes system in [0, T) × Ω, with initial value u0 ∈ L2σ(Ω) and external force f = div F, F ∈ L2(0, T;L2(Ω)). Our aim is to extend the well-known class of Leray-Hopf weak solutions u satisfying u{pipe}∂Ω = 0, div u = 0 to the more general class of Leray-Hopf type weak solutions u with general data u{pipe}∂Ω = g, div u = k satisfying a certain energy inequality. Our method rests on a perturbation argument writing u in the form u = υ + E with some vector field E in [0, T) × Ω satisfying the (linear) Stokes system with f = 0 and nonhomogeneous data. This reduces the general system to a perturbed Navier-Stokes system with homogeneous data, containing an additional perturbation term. Using arguments as for the usual Navier-Stokes system we get the existence of global weak solutions for the more general system.
Original language | English |
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Pages (from-to) | 51-70 |
Number of pages | 20 |
Journal | Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova |
Volume | 125 |
DOIs | |
Publication status | Published - 2011 |
Externally published | Yes |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Mathematical Physics
- Geometry and Topology