Blowups of complex-valued solutions for some hydrodynamic models
- First Online:
- 82 Downloads
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.
Key wordsblowup renormalization group method
Unable to display preview. Download preview PDF.
- 2.Li, D. and Sinai, Ya.G., Complex Singularities of the Burgers System and Renormalization Group Method, Current Developments in Mathematics, 2006, Somerville, MA: Int. Press, 2008, pp. 181–210.Google Scholar
- 7.Ladyzenskaya, O.A., Solonikov, V.A., and Uraltzeva, N.N., Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc. Transl. Monogr., vol. 23, Providence: AMS, 1968.Google Scholar