Global Regularity for General Non-Linear Wave Equations I. (6+1) and Higher Dimensions

Details Global Regularity for General Non-Linear Wave Equations I. (6+1) and Higher Dimensions Global Regularity for General Non-Linear Wave Equations I. (6+1) and Higher Dimensions

2004-02-12

arxiv.org/abs/math/0402193v1

Mathematics

Analysis of PDEs

24 pages, 2 figures

Scientific paper

We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative non-linearities are globally well posed in (6+1) and higher dimensions for all regularities greater than the scaling. This paper is the first in a series of works where we discuss the global regularity properties of general non-linear wave equations for all spatial dimensions greater than or equal to 4.

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