Vera Hur

Abstract: The motion of fluids can be complicated, as we know when we see waves break on a beach, fly in an airplane, or look at a lake on a windy day. Euler in the 1750s proposed a mathematical model for incompressible fluids, and since then an immense amount of progress has been made. But huge problems are still beyond our reach. Surface water waves refer to the situation where the water lies below a body of air. Describing what we may see or feel at the beach or in a boat, water waves are a perfect specimen of applied mathematics. They host a wealth of phenomena, ranging in length scale from ripples driven by surface tension to tsunamis and to rogue waves. I will review some recent developments in the mathematical aspects of water wave phenomena. Specifically,

(1) is there a unique solution to the Cauchy problem? for how long a time does it exist?

(2) are the solutions regular or do singularities form after some time?

(3) are there solutions spatially periodic? are they dynamically stable?

Here are some directions to Northeastern University. Lake Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from one of NEU colloquium organizers.