Mathematical Research Letters

Volume 6 (1999)

Number 5

On the equation $\Box u = |\nabla u|^2$ in $5+1$ dimensions

Pages: 469 – 485

DOI: http://dx.doi.org/10.4310/MRL.1999.v6.n5.a1

Author

Daniel Tataru (Northwestern University)

Abstract

The aim of this article is to complete the local theory for one of the most resilient semilinear hyperbolic equations. The main difficulty in such problems is to construct the function spaces in which we seek the solutions. Such spaces must, on one hand, be large enough, so that they contain the solutions; but on the other hand, they must be small enough, so that they have suitable multiplicative properties.

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