Strong 𝐿^{𝑝}-solutions to the Navier-Stokes flow past moving obstacles: The case of several obstacles and time dependent velocity

Dintelmann, Eva; Geissert, Matthias; Hieber, Matthias

doi:10.1090/S0002-9947-08-04684-9

Strong $L^p$-solutions to the Navier-Stokes flow past moving obstacles: The case of several obstacles and time dependent velocity
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by Eva Dintelmann, Matthias Geissert and Matthias Hieber PDF

Trans. Amer. Math. Soc. 361 (2009), 653-669 Request permission

Abstract:

Consider the Navier-Stokes flow past several moving or rotating obstacles with possible time-dependent velocity. It is shown that under suitable assumptions on the data, there exists a unique, local strong solution in the $L^p-L^q$-setting for suitable $p,q \in (1,\infty )$. Moreover, it is proved that this strong solution coincides with the known mild solution in the very weak sense.

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