Finite-time blowup for a supercritical defocusing nonlinear wave system (Q505927)

This paper studies the global regularity problem for a supercritical defocusing nonlinear wave system \(\square u=(\nabla_{\left(\mathbb R^m\right)}F)(u)\) on Minkowski space-time \(\mathbb R^{(1+d)}\) with a smooth potential \(F\) which is positive and homogeneous of order \(p+1\) outside of the unit ball for some \(p>1\). The author show, in the supercritical as \(d=3\) and \(p>5\), there exists a defocusing smooth potential F that is homogeneous of order \(p+1\) outside of the unit ball, and smooth initial data \(u(0)\) and \(\partial_tu(0)\), such that there is no global smooth solution to the nonlinear wave system with these choice for some large \(m\). Moreover, the singularity constructed is a discretely self-similar blowup in a backwards light one. The restriction to large value of \(m\) is due to the technical reason.