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We study the existence of SU(2)2-invariant G2-instantons on R4×S3 with the coclosed G2-structures found on 1. We find an explicit 1-parameter family of SU(2)3-invariant G2-instantons on the trivial bundle on R4×S3 and study its "bubbling" behaviour. We prove the existence a 1-parameter family on the identity bundle. We also provide existence results for locally defined SU(2)2-invariant G2-instantons.
Izar Alonso (Sat,) studied this question.