Local \(\varepsilon\)-regularity criteria for the five dimensional stationary Navier-Stokes equations. (English) Zbl 1515.35181
Summary: We establish interior and boundary \(\varepsilon\)-regularity criteria at one scale for suitable weak solutions to the five dimensional stationary incompressible Navier-Stokes equations which improve previous results in [K. Kang, J. Math. Fluid Mech. 6, No. 1, 78–101 (2004; Zbl 1050.35069)] and [M. Struwe, Commun. Pure Appl. Math. 41, No. 4, 437–458 (1988; Zbl 0632.76034)]. Our proof is based on an iteration argument, Campanato’s method, and interpolation techniques.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35D30 | Weak solutions to PDEs |
Keywords:
stationary Navier-Stokes equations; suitable weak solutions; \(\varepsilon\)-regularity criteria; interior estimates; boundary estimatesReferences:
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