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We establish new global well-posedness results along Gibbs measure evolutionfor the nonlinear wave equation posed on the unit ball in $\mathbb{R}^3$ viatwo distinct approaches. The first approach invokes the method established inthe works \cite{B1,B2,B3} based on a contraction-mapping principle and appliesto a certain range of nonlinearities. The second approach allows to cover thefull range of nonlinearities admissible to treatment by Gibbs measure, workinginstead with a delicate analysis of convergence properties of solutions. Themethod of the second approach is quite general, and we shall give applicationsto the nonlinear Schr\"odinger equation on the unit ball in subsequent works\cite{BB1,BB2}.

Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3D ball