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Transactions of the American Mathematical Society

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Existence of weak solutions for the Navier-Stokes equations with initial data in $ L\sp p$


Author: Calixto P. Calderón
Journal: Trans. Amer. Math. Soc. 318 (1990), 179-200
MSC: Primary 35Q10; Secondary 35D05, 76D05
DOI: https://doi.org/10.1090/S0002-9947-1990-0968416-0
Addendum: Trans. Amer. Math. Soc. 318 (1990), 201-207.
MathSciNet review: 968416
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Abstract: The existence of weak solutions for the Navier-Stokes equations for the infinite cylinder with initial data in $ {L^p}$ is considered in this paper. We study the case of initial data in $ {L^p}({R^n})$, $ 2 < p < n$, and $ n = 3,4$. An existence theorem is proved covering these important cases and therefore, the "gap" between the Hopf-Leray theory $ (p = 2)$ and that of Fabes-Jones-Riviere $ (p > n)$ is bridged. The existence theorem gives a new method of constructing global solutions. The cases $ p = n$ are treated at the end of the paper.


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DOI: https://doi.org/10.1090/S0002-9947-1990-0968416-0
Article copyright: © Copyright 1990 American Mathematical Society

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