## Spacetimes bounds for the energy-critical nonlinear wave equation in three spatial dimensions.(English)Zbl 1145.35089

The author improves the estimate of the $$L^{4}_{t}L^{12}_{x}(\mathbb R\times \mathbb R^{3})$$ norm of a global solution to the Cauchy problem for the equation $$u_{tt}-\Delta u=u^{5}.$$ The norm is bounded by the explicit function of the energy.

### MSC:

 35L70 Second-order nonlinear hyperbolic equations 35L15 Initial value problems for second-order hyperbolic equations 35B45 A priori estimates in context of PDEs

### Keywords:

global well-posedness; scattering
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