Geodesic
On solutions with infinite energy and enstrophy of the Navier--Stokes system
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 6, pp. 1061-1078

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The Cauchy problem is considered for the Navier–Stokes system. Local and global existence and uniqueness theorems are given for initial data whose Fourier transform decays at infinity as a power-law function with negative exponent and has a power-law singularity at zero. The paper contains a survey of known facts and some new results. 
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     author = {Yu. Yu. Bakhtin and E. I. Dinaburg and Ya. G. Sinai},
     title = {On solutions with infinite energy and enstrophy of the {Navier--Stokes} system},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {1061--1078},
     publisher = {mathdoc},
     volume = {59},
     number = {6},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2004_59_6_a3/}
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Yu. Yu. Bakhtin; E. I. Dinaburg; Ya. G. Sinai. On solutions with infinite energy and enstrophy of the Navier--Stokes system. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 6, pp. 1061-1078. http://geodesic.mathdoc.fr/item/RM_2004_59_6_a3/