Cathleen S. Morawetz, a mathematician whose theorems often found use in solving real-world engineering problems, died on Tuesday at her home in Manhattan. She was 94.

Her death was reported by New York University, where she had been a professor.

Much of Dr. Morawetz’s research centered on equations that describe the motion of fluids and waves — in water, sound, light and vibrating solids. One of her first notable papers helped explain the flow of air around airplanes flying close to the speed of sound.

Although the aircraft itself does not break the sound barrier, she found, some of the air rushing around the curves of its wings goes supersonic. Below the speed of sound, air flows in a fundamentally different manner than at supersonic speeds, and the mix of the two speeds — called transonic flight — produces shock waves that slow the aircraft.

Wings can be designed so that transonic airflow remains smooth at certain speeds without generating shock waves. But Dr. Morawetz’s work demonstrated that such shock-free wings do not work in the real world. The slightest perturbation — an imperfection in the shape, a tilt in the angle of the wing, a gust of wind — disrupts the smooth flow.