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2013
Impact Factor

# Yakov Sinai

Princeton NJ 08544 USA
Ak. Semenova av. 1-A, Moscow Region, Chernogolovka 142432, Russia
Mathematics Department, Princeton University
Landau Institute of Theoretical Physics

## Publications:

 Li D., Sinai Y. G. Blowups of complex-valued solutions for some hydrodynamic models 2010, vol. 15, no. 4-5, pp.  521-531 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. Keywords: blowup, renormalization group method Citation: Li D., Sinai Y. G.,  Blowups of complex-valued solutions for some hydrodynamic models, Regular and Chaotic Dynamics, 2010, vol. 15, no. 4-5, pp. 521-531 DOI:10.1134/S1560354710040088
 Li D., Sinai Y. G. Asymptotic Behavior of Generalized Convolutions 2009, vol. 14, no. 2, pp.  248-262 Abstract We study the behavior of a class of convolution-type nonlinear transformations. Under some smallness conditions we prove the existence of fixed points and analyze the spectrum of the associated linearized operator. Keywords: convolution, fixed point, Hermite polynomials Citation: Li D., Sinai Y. G.,  Asymptotic Behavior of Generalized Convolutions, Regular and Chaotic Dynamics, 2009, vol. 14, no. 2, pp. 248-262 DOI:10.1134/S1560354709020051
 Sinai Y. G. On a separating solution of a recurrent equation 2007, vol. 12, no. 5, pp.  490-501 Abstract We consider the recurrent equation $\Lambda_p = \frac{1}{p-1} \sum\limits_{p_1=1}^{p-1} f (\frac{p1}{p}) \Lambda_{p_1} · \Lambda_{p-p_1}$ which depends on the initial condition $\Lambda_1=x$. Under some conditions on $f$ we show that there exists the value of x for which $\Lambda_p$ tends to a constant as p tends to infinity. Keywords: separating solution, recurrent equation Citation: Sinai Y. G.,  On a separating solution of a recurrent equation, Regular and Chaotic Dynamics, 2007, vol. 12, no. 5, pp. 490-501 DOI:10.1134/S1560354707050036
 Sinai Y. G. Navier–Stokes systems with periodic boundary conditions 1999, vol. 4, no. 2, pp.  3-15 Abstract The article presents a review of geometrical proof of the results earlier obtained by Foias, Temam with respect to Gevre class regularity for the solution of the Navier–Stokes equations. The articleis based on the lectures, delivered at the Moscow Independent University in june 1999. Citation: Sinai Y. G.,  Navier–Stokes systems with periodic boundary conditions, Regular and Chaotic Dynamics, 1999, vol. 4, no. 2, pp. 3-15 DOI:10.1070/RD1999v004n02ABEH000108