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We present regularity conditions for suitable weak solutions of the Navier-Stokes equations with slip boundary data near the curved boundary. To be more precise, we prove that suitable weak solutions become regular in a neighborhood boundary points, provided the scaled mixed norm $L^{p,q}_{x,t}$ with $3/p+2/q=2$, $1\leq q<\infty$ is sufficiently small in the neighborhood.
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참고문헌 (36)
참고문헌 신청
S. N. Antontsev / 2007 / Navier-Stokes equations with absorption under slip boundary conditions: existence, uniqueness and extinction in time / Kyoto Conference on the Navier-Stokes Equations and their Applications :21~41
H. Bae / 2008 / Pressure representation and boundary regularity of the Navier-Stokes equations with slip boundary condition / J. Differential Equations 244(11):2741~2763
H. Beir˜ao da Veiga / 2005 / On the regularity of flows with Ladyzhenskaya shear-dependent viscosity and slip or nonslip boundary conditions / Comm. Pure Appl. Math 58(4):771~831
L. Caffarelli / 1982 / Partial regularity of suitable weak solutions of the Navier-Stokes equations / Comm. Pure Appl. Math 35(6):771~831
H. Choe / 2000 / On the singular set in the Navier-Stokes equations / J. Funct. Anal 175(2):348~369
H. Bae / 2008 / Pressure representation and boundary regularity of the Navier-Stokes equations with slip boundary condition / J. Differential Equations 244(11):2741~2763
H. Beir˜ao da Veiga / 2005 / On the regularity of flows with Ladyzhenskaya shear-dependent viscosity and slip or nonslip boundary conditions / Comm. Pure Appl. Math 58(4):771~831
L. Caffarelli / 1982 / Partial regularity of suitable weak solutions of the Navier-Stokes equations / Comm. Pure Appl. Math 35(6):771~831
H. Choe / 2000 / On the singular set in the Navier-Stokes equations / J. Funct. Anal 175(2):348~369
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