## Strong $$L^ p$$-solutions of the Navier-Stokes equation in $$R^ m$$, with applications to weak solutions.(English)Zbl 0545.35073

See the preview in Zbl 0537.35065.

### MSC:

 35Q30 Navier-Stokes equations 35A07 Local existence and uniqueness theorems (PDE) (MSC2000) 35B40 Asymptotic behavior of solutions to PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs

Zbl 0537.35065
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### References:

 [1] Giga, Y.: Regularity criteria for weak solutions of the Navier-Stokes system. Proc. AMS Summer Inst. 1983, to appear · Zbl 0547.35101 [2] Kato, T., Fujita, H.: On the non-stationary Navier-Stokes system. Rend. Sem. Mat. Univ. Padova32, 243-260 (1962) · Zbl 0114.05002 [3] Leray, J.: ?tude de diverses ?quations int?grales non lin?aires et de quelques probl?mes que pose l’Hydrodynamique. J. Math. Pures Appl.12, 1-82 (1933) · Zbl 0006.16702 [4] Leray, J.: Sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math.63, 193-248 (1934) · JFM 60.0726.05 [5] Serrin, J.: The initial value problem for the Navier-Stokes equation. Nonlinear Problems, Proc. Symp. MRC, Univ. Wisconsin, Madison, 1963, pp. 69-98 · Zbl 0115.08502 [6] Sohr, H., von Wahl, W.: On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations. Sonderforschungsbereich 72 Approximation und Optimierung, Universit?t Bonn, Preprint series no. 635 (1984) · Zbl 0567.35069 [7] Weissler, F.: The Navier-Stokes initial value problem inL p . Arch. Rational Mech. Anal.74, 219-230 (1980) · Zbl 0454.35072
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