TY - JOUR
T1 - Complex Singular Solutions of the 3-d Navier–Stokes Equations and Related Real Solutions
AU - Boldrighini, Carlo
AU - Li, Dong
AU - Sinai, Yakov G.
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media New York.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267–313, 2008) proved that there are complex solutions of the Navier–Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267–313, 2008) to the study of the real ones.
AB - By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267–313, 2008) proved that there are complex solutions of the Navier–Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267–313, 2008) to the study of the real ones.
KW - Blow-up
KW - Global regularity
KW - Navier–Stokes equations
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U2 - 10.1007/s10955-017-1730-1
DO - 10.1007/s10955-017-1730-1
M3 - Review article
AN - SCOPUS:85011636475
SN - 0022-4715
VL - 167
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 1
ER -