Details

Autor(en) / Beteiligte

• Sin, Cholmin
• Baranovskii, Evgenii S.

Titel

Regularity criterion for 3D generalized Newtonian fluids in BMO

Ist Teil von

• Journal of Differential Equations, 2023-12, Vol.377, p.859-872

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2023

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we prove that a weak solution of the Cauchy problem for 3D unsteady flows of a generalized Newtonian fluid becomes a strong solution for 53<p<115 provided that the velocity field belongs to the critical space L2p−1(0,T;BMO(R3)). The main key is to apply variants of Gagliardo–Nirenberg's inequality including a BMO-norm. In particular, when 2<p<115, we derive and use a nonlinear variant of Gagliardo–Nirenberg's inequality including ‖u‖BMO and ‖|Du|p−22∇2u‖2.