Local existence with minimal regularity for nonlinear wave equations
- 1 June 1997
- journal article
- research article
- Published by Project MUSE in American Journal of Mathematics
- Vol. 119 (3) , 671-703
- https://doi.org/10.1353/ajm.1997.0020
Abstract
In this paper, we consider the Cauchy problem of semilinear wave equations which satisfy the "null condition." We prove that the problem is locally well-posed in Hs+1 for s > ¾ in 1 + 3 dimensions and s > ¼ in 1 + 2 dimensions. Moreover, it is shown that the result in 1 + 2 dimensions is sharp.Keywords
This publication has 2 references indexed in Scilit:
- Space‐time estimates for null forms and the local existence theoremCommunications on Pure and Applied Mathematics, 1993
- On local existence for nonlinear wave equations satisfying variable coefficient null conditionsCommunications in Partial Differential Equations, 1993