On boundary-driven time-dependent Oseen flows

• Autorzy: Paul Deuring
• Języki publikacji: EN

Abstrakty

EN

We consider the single layer potential associated to the fundamental solution of the time-dependent Oseen system. It is shown this potential belongs to L²(0,∞,H¹(Ω)³) and to H¹(0,∞,V') if the layer function is in L²(∂Ω×(0,∞)³). (Ω denotes the complement of a bounded Lipschitz set; V denotes the set of smooth solenoidal functions in H¹₀(Ω)³.) This result means that the usual weak solution of the time-dependent Oseen function with zero initial data and zero body force may be represented by a single layer potential, provided a certain integral equation involving the boundary data may be solved.

Kategorie tematyczne

• 35C15: Integral representations of solutions
• 35Q30: Navier-Stokes equations
• 76D07: Stokes and related (Oseen, etc.) flows

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 119-132

Daty

wydano

2008

Twórcy

autor

Paul Deuring

• Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral, B.P. 699, 62228 Calais, France

Identyfikatory

DOI

10.4064/bc81-0-8