Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations
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In this paper we show that after suitable data randomization there exists a large set of supercritical periodic initial data, in $H^{-\alpha}(\boldsymbol{T}^d)$ for some $\alpha(d) > 0$, for both two- and three-dimensional Navier--Stokes equations for which global energy bounds hold. As a consequence, we obtain almost sure large data supercritical global weak solutions. We also show that in two dimensions these global weak solutions are unique.
Date issued
2013-01Department
Massachusetts Institute of Technology. Department of MathematicsJournal
SIAM Journal on Mathematical Analysis
Publisher
Society for Industrial and Applied Mathematics
Citation
Nahmod, Andrea R., Nataša Pavlović, and Gigliola Staffilani. “Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations.” SIAM J. Math. Anal. 45, no. 6 (January 2013): 3431–3452.
Version: Final published version
ISSN
0036-1410
1095-7154