Unconditional well-posedness for the energy-critical nonlinear damped wave equation

Abstract

For the energy-critical nonlinear damped wave equation, we show the unconditional wellposedness. The unconditional well-posedness means local well-posedness and the unconditional uniqueness. First, we give the local well-posedness and stability, whose statement will be useful to investigate the global dynamics. At second, we show the unconditional uniqueness. Since these problems seem not to be solvable as a direct perturbation of the wave equation, we apply the Strichartz estimates for the damped wave equation including the wave endpoint case. 4 d−2 w.(NLW)These equations are invariant under the scaling:2 w(λt, λx),