Weak solutions for the Oseen system in 2D and when the given velocity is not sufficiently regular

Chérif Amrouche (1) , M A Rodríguez-Bellido

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

The aim of this work is twofold: proving the existence of solution (u, π) ∈ H 1 (Ω)×L 2 (Ω) in bounded domains of R 2 and the whole plane for the Oseen problem (O) for solenoidal vector fields v in L 2 (Ω), and analyzing the same problem in bounded domains of R n for n = 2, 3 when h = 0, g = 0 and the solenoidal field v belongs to L s (Ω) for s < n.

Mots clés: Oseen equations; stationary solutions; irregular data; Hardy spaces 2010 MSC: 35Q35; 25J15; 76D03; 76D07

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Chérif Amrouche, M A Rodríguez-Bellido. Weak solutions for the Oseen system in 2D and when the given velocity is not sufficiently regular. Applied Mathematics Letters, 2019. ⟨hal-02494791⟩