Linear profile decompositions for a family of fourth order Schrödinger equations (1410.7520v2)

Published 28 Oct 2014 in math.AP and math.CA

Abstract: We establish linear profile decompositions for the fourth order Schr\"odinger equation and for certain fourth order perturbations of the Schr\"odinger equation, in dimensions greater than or equal to two. We apply these results to prove dichotomy results on the existence of extremizers for the associated Stein--Tomas/Strichartz inequalities; along the way, we also obtain lower bounds for the norms of these operators.

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