Your question pertains to the legal sanctity and enforceability of a divorce decree of a U.S. court in India if I am not wrong. Please do correct me in case I am.
Such a decree of divorce is per se not valid in India—at least not until it has been tested on the touchstone of Section 13 of the CPC. The long and short of it is that the Court there is not one of competent jurisdiction for the purposes of the Hindu Marriage Act and “irretrievable breakdown” not a valid ground of divorce, and for these reasons any divorce decree by a U.S. court isn’t valid in India.
But if both parties to the marriage voluntarily submit themselves to the jurisdiction of a foreign court for the purpose of divorce, neither can come to India and say that the foreign court did not have jurisdiction. In that case, a decree will be held to be valid.
All said, a decree of a U.S. court cannot be executed as is in India. You will have to bring a suit based on that decree in what is a rather roundabout manner of getting Indian courts to recognise it.
Further questions are welcome.