## Global well-posedness for semilinear wave equations.(English)Zbl 0961.35092

The authors prove global well-posedness of the Cauchy problem associated to the equation $$u_{tt}-\triangle u=-|u|^{p-1}u$$, $$t\in \mathbb{R}$$, $$x\in \mathbb{R}^3$$, $$p\in (2,5),$$ under minimal regularity assumptions on the initial data.

### MSC:

 35L70 Second-order nonlinear hyperbolic equations 35D10 Regularity of generalized solutions of PDE (MSC2000) 35L15 Initial value problems for second-order hyperbolic equations 35B45 A priori estimates in context of PDEs
Full Text:

### References:

 [1] DOI: 10.1155/S1073792898000191 · Zbl 0917.35126 [2] Bourgain. J., New global well-posedness results for the nonlinear Schrödinger equations, pre-print [3] DOI: 10.1155/S107379289800066X · Zbl 0999.58013 [4] DOI: 10.1002/cpa.3160460902 · Zbl 0803.35095 [5] DOI: 10.1215/S0012-7094-93-07219-5 · Zbl 0797.35123 [6] DOI: 10.1006/jfan.1995.1075 · Zbl 0846.35085 [7] DOI: 10.1007/BF01181697 · Zbl 0538.35063 [8] DOI: 10.1215/S0012-7094-97-08604-X · Zbl 0874.35114 [9] DOI: 10.1215/S0012-7094-77-04430-1 · Zbl 0372.35001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.