Large-data local well-posedness under nontrapping conjecture

Let $s$ denote the Sobolev regularity exponent, and let Theorems~ and be the stated local well-posedness results for the two-dimensional and $n$-dimensional cubic problems. Large-data local well-posedness under nontrapping conjecture. Those results also hold for large data, under an additional nontrapping assumption. The claim proposes extending the small-data local theory to large data when geometric trapping is excluded; the source presents it as a related open conjecture.