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Some asymptotic problems in fluid mechanics. (English) Zbl 0977.35109
Lumer, G√ľnter (ed.) et al., Evolution equations and their applications in physical and life sciences. Proceeding of the Bad Herrenalb (Karlsruhe) conference, Germany, 1999. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 215, 395-404 (2001).
This short review paper summarizes results of an asymptotic nature from the field of fluid mechanics. Such problems arise when a dimensionless parameter related to some physical property tends to zero in an equation, usually causing a fundamental change in the nature of the solution. Issues considered briefly are the nature of the convergence of solutions as such parameters tend to zero, and the possibility that the use of the notion of weak convergence can provide more information about issues like the occurrence of oscillations. The majority of the paper is concerned with an examination of the Navier-Stokes Euler limit.
For the entire collection see [Zbl 0957.00037].

MSC:
35Q35 PDEs in connection with fluid mechanics
35Q05 Euler-Poisson-Darboux equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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