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Keywords:
Navier-Stokes equations; weak solution; regularity
Navier-Stokes equations; weak solution; regularity
Summary:
Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space $L^2(0,T,W^{1,3}(\varOmega)^3)$ are regular.
References:
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[2] Kato T.: Perturbation Theory for Linear Operators. Springer-Verlag, Berlin, Heidelberg, New York 1980. Zbl 0836.47009
[3] Kozono H.: Uniqueness and regularity of weak solutions to the Navier-Stokes equations. Lecture Notes in Num. and Appl. Anal. 16 (1998), 161-208. MR 1616331 | Zbl 0941.35065
[4] Neustupa J.: Partial regularity of weak solutions to the Navier-Stokes Equations in the class $L^\infty(0,T,L^3(\varOmega))$. J. Math. Fluid Mech. 1 (1999), 1-17. MR 1738173
[5] Serrin J.: On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal. 9 (1962), 187-195. MR 0136885 | Zbl 0106.18302
[6] Temam R.: Navier-Stokes Equations, Theory and Numerical Analysis. North-Holland Publishing Company, Amsterdam, New York, Oxford, 1979. MR 0603444 | Zbl 0981.35001
[7] Temam R.: Navier-Stokes Equations and Nonlinear Functional Analysis. Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, second edition, 1995. MR 1318914 | Zbl 0833.35110
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