A study on blowup solutions to the focusing L2-supercritical nonlinear fractional Schrodinger equation

We study the dynamical properties of blowup solutions to the focusing L-2-supercritical nonlinear fractional Schrodinger equation i partial derivative(t)u - (-Delta)(s)u = -vertical bar u vertical bar(alpha)u on [0, +infinity) x R-d, where d >= 2, d/2d-1 <= s < 1, 4s/d < alpha < 4s/d-2s, and the initial data u(0) = u(0) is an element of <(H)over dot>(Sc) boolean AND <(H)over dot>(S) is radial with the critical Sobolev exponent S-c. To this end, we establish a compactness lemma related to the equation by means of the profile decomposition for bounded sequences in <(H)over dot>(Sc) boolean AND <(H)over dot>(S). As a result, we obtain the <(H)over dot>(Sc)-concentration of blowup solutions with bounded <(H)over dot>(Sc)-norm and the limiting profile of blowup solutions with critical <(H)over dot>(Sc)-norm. Published by AIP Publishing.