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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
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