Constructing two-bubble solutions for the equivariant energy-critical wave maps equation
Abstract：I consider the wave maps equation from R^(1+2) to S^2. This equation is energy-critical, which means it potentially allows energy concentration through “bubbling”. I construct solutions with equivariant symmetry which exist for all positive times and converge to a superposition of two rescaled stationary solutions (“bubbles”) as time goes to infinity. The scale of one of these bubbles converges to 0 at a specific rate, whereas the scale of the other remains fixed. These solutions play the role of threshold non-dispersive objects for equivariant initial data.