On interior regularity criteria for weak solutions of the Navier-Stokes equations. (English) Zbl 0718.35022
In this paper some results on interior regularity of weak solution for certain parabolic system in spaces \(L^{p,q}(Q)\) are obtained under minimal regularity assumptions on the coefficients.
Applying the above results for the vorticity equations, there are obtained new local interior regularity criteria for weak solutions of the time-dependent Navier-Stokes equations for an incompressible medium with the adherence property to the smooth boundary of the considered domain in \(R^ n\) (n\(\geq 3).\)
A priori estimates for weak solutions of a Cauchy problem of some linear parabolic nonhomogeneous system with nonregular coefficients in \(R^ n\times (0,T)\) are also obtained using cut-off functions instead of traces in Sobolev spaces of negative order.
Applying the above results for the vorticity equations, there are obtained new local interior regularity criteria for weak solutions of the time-dependent Navier-Stokes equations for an incompressible medium with the adherence property to the smooth boundary of the considered domain in \(R^ n\) (n\(\geq 3).\)
A priori estimates for weak solutions of a Cauchy problem of some linear parabolic nonhomogeneous system with nonregular coefficients in \(R^ n\times (0,T)\) are also obtained using cut-off functions instead of traces in Sobolev spaces of negative order.
Reviewer: M.Rodriguez Ricard (Ciudao de La Habana)
MSC:
| 35D10 | Regularity of generalized solutions of PDE (MSC2000) |
| 35Q30 | Navier-Stokes equations |
Keywords:
interior regularityReferences:
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