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Navier-Stokes flow in \(R^ 3\) with measures as initial vorticity and Morrey spaces. (English) Zbl 0681.35072
The authors study the vorticity equations, derived from the unsteady, incompressible Navier-Stokes equations, with initial data in Morrey spaces. Under suitable smallness assumptions they prove the existence of a unique smooth global solution.
Reviewer: G.Warnecke

MSC:
35Q30 Navier-Stokes equations
35J25 Boundary value problems for second-order elliptic equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] DOI: 10.1016/0362-546X(85)90039-2 · Zbl 0621.76027
[2] Campanato S., Ricerche Mat 12 pp 67– (1963)
[3] Campanato S., Ann. Scuola Norm. Sup. Pisa 17 pp 175– (1963)
[4] Campanato S., Ann. Scuola Norm. Sup. Pisa 18 pp 137– (1964)
[5] DOI: 10.1007/BF02414377 · Zbl 0145.36603
[6] DOI: 10.1007/BF02415082 · Zbl 0144.14101
[7] DOI: 10.1007/BF02416805 · Zbl 0183.41201
[8] Cottet G. –H., C. R. Acad. Sci. Paris 303 pp 105– (1986)
[9] Federer H., Geometric measure theory (1969) · Zbl 0176.00801
[10] DOI: 10.1103/PhysRevLett.51.617
[11] Friedman A., Partial differential equations (1969)
[12] DOI: 10.1007/BF00276188 · Zbl 0126.42301
[13] Giaquinta, M. 1983. ”Multiple integrals in the calculus of variations and nonlinear elliptic systems”. Vol. 105, Princeton: Princeton University Press. · Zbl 0516.49003
[14] DOI: 10.1016/0022-0396(86)90096-3 · Zbl 0577.35058
[15] Giga Y., Arch. Rational Mech. Anal
[16] Giga Y.., Commun. Math. Phys
[17] Gilbarg D., Elliptic partial differential equations of second order · Zbl 0361.35003
[18] DOI: 10.1512/iumj.1982.31.31016 · Zbl 0465.35049
[19] DOI: 10.1002/cpa.3160140317 · Zbl 0102.04302
[20] DOI: 10.1007/BF01162027 · Zbl 0607.35072
[21] DOI: 10.1007/BF01174182 · Zbl 0545.35073
[22] Morrey C.B., Multiple integrals in the calculus of variation (1966) · Zbl 0142.38701
[23] DOI: 10.1016/0022-1236(69)90022-6 · Zbl 0175.42602
[24] Reed M., Methods of modern mathematical physics Vol II; Fourier analysis, self-adjointness (1975)
[25] DOI: 10.1080/03605308608820443 · Zbl 0607.35071
[26] Simon L., Proc. Center for Math. Anal 3 (1983)
[27] Stein E.M., Introduction to Fourier analysis on Euclidean spaces (1971)
[28] von Wahl W., The equations of Navier-Stokes and abstract parabolic equations (1985) · Zbl 0575.35074
[29] DOI: 10.1112/jlms/s2-35.2.303 · Zbl 0652.35095
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