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Dong Li

14 MacLean Hall, Iowa City, IA 52242
Department of Mathematics, University of Iowa


Li D., Sinai Y. G.
Blowups of complex-valued solutions for some hydrodynamic models
2010, vol. 15, no. 4-5, pp.  521-531
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
Li D., Sinai Y. G.
Asymptotic Behavior of Generalized Convolutions
2009, vol. 14, no. 2, pp.  248-262
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

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