Uh, does a car going a hundred and thirty miles an hour suddenly stop if it runs out of gas? No Cat 3 storm falls apart immediately upon landfall. Heck, Katrina came ashore in Florida as a Cat 1, and she tracked all across Miami-Dade County from northeast to southwest without losing one single mph.
Florida is a relatively narrow peninsula and some of the hurricane was able to draw strength from being over the Gulf or the Atlantic. Even when Katrine hit LA it went from a 4 to a 1 almost immediately. Without the heat source the rotation slows as cooler air is drawn up into the eye. I didn't mean to say the storm would go away. I used the term "fall apart" as a relative term to what it was while over the warm waters of the Gulf.