It's unlikely that they want to hold on to Ukraine. They have recognized Donetsk and Lugansk and will protect their borders but their stated intent with Ukraine is to "demilitarize" them. If they have any sense they will demolish every military asset they can find and then get out. They will unfortunately probably kill a large number of soldiers and people relevant to their political interests as well. I just hope they can avoid mass civilian casualties.

Putin has stated that he views Ukrainian membership in NATO and the presence of NATO forces on their border as an existential threat to Russia so that is at least the public reason that they are doing this. If we take that at face value then the objective is to destabilize Ukraine to the point where they are ineligible to join NATO for a long time. That doesn't bode well for the Ukrainian people.