Indeed, Arwen does decide to come back to Aragorn just a few days later. She marries him, thereby becoming mortal. The last of the Fellowship who were staying with King Elessar and Queen Arwen ...

And it is after this war has ended that "Aragorn the King Elessar wedded Arwen Undomiel in the City of the Kings...and the tale of their long waiting and labours was come to fulfillment." ...