Solvability of the Cauchy problem of nonlinear beam equations in Besov spaces Original Research Article

In this paper we study solvability of the Cauchy problem of the nonlinear beam equation View the MathML source∂t2u+△2u=±up with initial data in Besov spaces. We prove that, for any 1≤q<∞1≤q<∞, the Cauchy problem of this equation is locally well-posed in the Besov spaces View the MathML sourceḂ2,qsp(Rn) and View the MathML sourceB2,qs(Rn), where View the MathML sourcesp=n2−4p−1 and s>sps>sp, and globally well-posed in these spaces if initial data are small. Moreover we obtain scattering results in View the MathML sourceḂ2,qsp(Rn).