Abstract:
We study complex-valued blowups of solutions for several hydrodynamic models. For complex-valued initial conditions, smooth local solutions can have finite-time singularities since the energy inequality does not hold. By using some version of the renormalization group method, we derive the equations for corresponding fixed points and analyze the spectrum of the linearized operator. We describe the open set of initial conditions for which blowups at finite time can occur.
\Bibitem{LiSin10}
\by D. Li, Ya. G. Sinai
\paper Blowups of complex-valued solutions for some hydrodynamic models
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 4-5
\pages 521--531
\mathnet{http://mi.mathnet.ru/rcd513}
\crossref{https://doi.org/10.1134/S1560354710040088}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2679762}
\zmath{https://zbmath.org/?q=an:1205.35227}
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This publication is cited in the following 7 articles:
Denis Gaidashev, Alejandro Luque, “Renormalization and Existence of Finite-Time Blow-Up Solutions for a One-Dimensional Analogue of the Navier–Stokes Equations”, SIAM J. Math. Anal., 56:4 (2024), 4356
Boldrighini C., Frigio S., Maponi P., Pellegrinotti A., Sinai Ya.G., “An Antisymmetric Solution of the 3D Incompressible Navier-Stokes Equations With “Tornado-Like” Behavior”, J. Exp. Theor. Phys., 131:2 (2020), 356–360
Carlo Boldrighini, Dong Li, Yakov G. Sinai, “Complex Singular Solutions of the 3-d Navier–Stokes Equations and Related Real Solutions”, J Stat Phys, 167:1 (2017), 1
C. Boldrighini, S. Frigio, P. Maponi, “On the blow-up of some complex solutions of the 3D Navier–Stokes equations: theoretical predictions and computer simulations”, IMA Journal of Applied Mathematics, 82:4 (2017), 697
The Navier-Stokes Problem in the 21st Century, 2016, 677
Jinxin Xue, Dmitry Dolgopyat, “Non-Collision Singularities in the Planar Two-Center-Two-Body Problem”, Commun. Math. Phys., 345:3 (2016), 797
C. Boldrighini, S. Frigio, P. Maponi, “Exploding solutions of the complex two-dimensional Burgers equations: Computer simulations”, Journal of Mathematical Physics, 53:8 (2012)
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