Search results for "Prandtl’s equations"

showing 2 items of 2 documents

Singularity tracking for Camassa-Holm and Prandtl's equations

2006

In this paper we consider the phenomenon of singularity formation for the Camassa-Holm equation and for Prandtl's equations. We solve these equations using spectral methods. Then we track the singularity in the complex plane estimating the rate of decay of the Fourier spectrum. This method allows us to follow the process of the singularity formation as the singularity approaches the real axis.

Essential singularityNumerical AnalysisCamassa–Holm equationApplied MathematicsComplex singularitieMathematical analysisPrandtl numberPrandtl’s equationsSingularity functionPrandtl–Glauert transformationComputational Mathematicssymbols.namesakeSpectral analysiSingularitysymbolsCamassa–Holm equationSpectral methodComplex planeMathematicsBoundary layer separation
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Singularities for Prandtl's equations.

2006

We used a mixed spectral/finite-difference numerical method to investigate the possibility of a finite time blow-up of the solutions of Prandtl's equations for the case of the impulsively started cylinder. Our toll is the complex singularity tracking method. We show that a cubic root singularity seems to develop, in a time that can be made arbitrarily short, from a class of data uniformely bounded in H^1.

Prandtl’s equations Separation Spectral methods Complex singularities Blow–up time Regularizing viscosity.Settore MAT/07 - Fisica Matematica
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