One component regularity for the Navier-Stokes equations. (English) Zbl 1149.35069

Kukavica, Igor; Ziane, Mohammed

Nonlinearity 19, No. 2, 453-469 (2006).

The authors show that regularity assumptions on one component of the velocity imply regularity of the full solution. These suffficient conditions are certain space-time regularity of the gradient of one component or the component itself. These conditions improve some other one component regularity results, e.g., in [J. Neustupa, A. Novotný and P. Penel, Topics in mathematical fluid mechanics. Meeting on the occasion of Professor John G. Heywood sixtieth birthday, Capo Miseno, Italy, May 27–30, 2000. Rome: Aracne. Quad. Mat. 10, 163–183 (2002; Zbl 1050.35073) and Applied nonlinear analysis. In honor of the 70th birthday of Professor Jindrich Nečas. New York, NY: Kluwer Academic/Plenum Publishers, 391–402 (1999; Zbl 0953.35113)].

Reviewer: Jens Rademacher (Amsterdam)

MSC:

35Q30	Navier-Stokes equations
35B65	Smoothness and regularity of solutions to PDEs
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05	Navier-Stokes equations for incompressible viscous fluids
35K15	Initial value problems for second-order parabolic equations

Keywords:

Navier-Stokes equations; regularity

Citations:

Zbl 1050.35073; Zbl 0953.35113