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The Navier-Stokes initial value problem in \(L^ p\). (English) Zbl 0454.35072

MSC:
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
[2] E. B. Fabes, B. F. Jones & N. M. Riviere, The initial value problem for the Navier-Stokes equations with data in L p .Arch. Rational Mech. Anal. 45 (1972), 222–240. · Zbl 0254.35097 · doi:10.1007/BF00281533
[3] E. B. Fabes, J. E. Lewis & N. M. Riviere, Singular integrals and hydrodynamic potentials. Am. Jour. of Math. 99 (1977), 601–625. · Zbl 0374.44006 · doi:10.2307/2373932
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[10] J. E. Lewis, The initial-boundary value problem for the Navier-Stokes equations with data in L p . Indiana U. Math. Jour. 22 (1973), 739–761. · Zbl 0252.35054 · doi:10.1512/iumj.1973.22.22060
[11] J. E. Marsden & M. McCracken, The Hopf Bifurcation and its Applications. Springer-Verlag, New York, 1976. · Zbl 0346.58007
[12] M. McCracken, The Stokes equations in L p , Doctoral Dissertation, University of California, Berkeley, 1975.
[13] R. Temam, Navier-Stokes Equations. North-Holland Publishing Company, New York, 1977. · Zbl 0383.35057
[14] F. B. Weissler, Semilinear evolution equations in Banach spaces. Jour. Func. Anal. 32 (1979), 277–296. · Zbl 0419.47031 · doi:10.1016/0022-1236(79)90040-5
[15] F. B. Weissler, Local existence and nonexistence for semilinear parabolic equations in L p . Indiana U. Math. Jour. 29 (1980), 79–102. · Zbl 0443.35034 · doi:10.1512/iumj.1980.29.29007
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