When a person does a thorough research on something, it means that they perform an examination on it to find out more about it. Another way of saying the sentence in the question therefore, is that Roosevelt examined Amelia Earhart.
The Roosevelt in question is probably Eleanor Roosevelt, wife of President Roosevelt and First Lady of the United States when Amelia Earhart made a name for herself as the first female aviator to cross the Atlantic Ocean flying solo.
The two were great friends and Eleanor probably researched Ms. Earhart's disappearance during a flight extensively.
