## High frequency approximation of solutions to critical nonlinear wave equations.(English)Zbl 0919.35089

Using scattering theory and structure theorem for bounded energy sequences of solutions to the wave equation, the authors give the description of bounded energy sequences of solutions of the Cauchy problem to the equation $$u_{tt}-(u_{xx}+u_{yy}+u_{zz})+| u| ^4u=0.$$ In particular, the existence of an a priori estimate of the Strichartz norms of solutions to the above equation in terms of their energy is proved.

### MSC:

 35L70 Second-order nonlinear hyperbolic equations 35B45 A priori estimates in context of PDEs 35B35 Stability in context of PDEs 35L15 Initial value problems for second-order hyperbolic equations

Strichartz norm
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