Blow‐up analysis and energy identities for super‐sinh‐Gordon‐type equation

Abstract We study blow‐up analysis for the super‐sinh‐Gordon‐type equation, which couples a function and a spinor field , a natural generalization of Liouville equation, super‐Liouville equation, and sinh‐Gordon equation. Here, is a parameter, and are ‐smooth functions defined on a closed Riemann surface . We establish refined qualitative properties for a blow‐up sequence of solutions to the super‐sinh‐Gordon‐type equation. In particular, we prove energy identities not only for the spinor part, but also for the function part. Moreover, the local masses at a blow‐up point are also computed. We show that if blow‐up phenomenon happens, then the parameter must go to zero. When reducing to the sinh‐Gordon equation (for ), this gives an affirmative answer to Problem 2 proposed by Jost–Wang–Ye–Zhou in 2008.