Existence of weak solutions for the Navier-Stokes equations with initial data in 𝐿^{𝑝}

Calderón, Calixto P.

doi:10.1090/S0002-9947-1990-0968416-0

Existence of weak solutions for the Navier-Stokes equations with initial data in $L^ p$
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by Calixto P. Calderón PDF

Trans. Amer. Math. Soc. 318 (1990), 179-200 Request permission

Addendum: Trans. Amer. Math. Soc. 318 (1990), 201-207.

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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Neuere Methoden und Ergebnisse in der Hydrodinamik

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