Open AccessProperties at potential blow-up times for Navier-Stokes
Author(s) -
Paulo R. Zingano,
Jens Lorenz
Publication year - 2017
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.v35i2.27508
Subject(s) - infinity , gravitational singularity , interval (graph theory) , mathematics , compressibility , navier–stokes equations , mathematical analysis , cauchy problem , initial value problem , physics , mechanics , combinatorics
In this paper we consider the Cauchy problem for the 3D navier-Stokes equations for incompressible flows. The initial data are assume d to be smooth and rapidly decaying at infinity. A famous open problem is whether classical solution can develop singularities in finite time. Assuming the maximal interval of existence to be finite, we give a unified discussion of various known solution properties as time approaches the blow-up time