## 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.## References

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## Additional Information

- © Copyright 1990 American Mathematical Society
- 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
- MathSciNet review: 968416