Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Unsteady asymptotic solutions of the two-dimensional Euler equations

Author: Radhakrishnan Srinivasan
Journal: Quart. Appl. Math. 54 (1996), 211-223
MSC: Primary 35Q35; Secondary 76C05
DOI: https://doi.org/10.1090/qam/1388013
MathSciNet review: MR1388013
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Abstract: A technique is described for deducing a class of unsteady asymptotic solutions of the two-dimensional Euler equations. In contrast to previously known analytical results, the vorticity function $ \left[ {\omega \left( {x, y, t} \right)} \right]$ for these solutions has a complicated dependence on the spatial coordinates $ \left( {x, y} \right)$ and time $ \left( t \right)$. The results obtained are in implicit form and are valid in those regions of space and time where $ t\omega \to {o^ + }$ or $ t\omega \to + \infty $. These asymptotic solutions may be split into an unsteady, two-dimensional and irrotational basic flow and a disturbance that is strongly nonlinear at appropriate locations within the domain of validity. The generality and complexity of these solutions make them theoretically interesting and possibly useful in applications.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/1388013
Article copyright: © Copyright 1996 American Mathematical Society

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