## 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

### Keywords:

Navier-Stokes equation; semigroup; initial value problem

Zbl 0126.423
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### References:

 [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 [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 [4] E. B. Fabes, J. E. Lewis & N. M. Riviere, Boundary value problems for the Navier-Stokes equations. Am. Jour. of Math. 99 (1977), 626–668. · Zbl 0386.35037 [5] A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, Inc., New York, 1969. · Zbl 0224.35002 [6] H. Fujita & T. Kato, On the Navier-Stokes initial value problem I. Arch. Rational Mech. Anal 16 (1964), 269–315. · Zbl 0126.42301 [7] T. Kato, Perturbation Theory for Linear Operators. Springer-Verlag, New York, 1966. · Zbl 0148.12601 [8] T. Kato & H. Fujita, On the nonstationary Navier-Stokes system. Rend. Sem. Mat. Univ. Padova 32 (1962), 243–260. · Zbl 0114.05002 [9] H. Komatsu, Fractional powers of operators. Pac. J. Math. 19 (1966), 285–346. · Zbl 0154.16104 [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 [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 [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
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