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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
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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
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