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Two dimensional gravity water waves at low regularity

[Moved Online] Recent Developments in Fluid Dynamics April 12, 2021 - April 30, 2021

April 15, 2021 (09:00 AM PDT - 09:50 AM PDT)
Speaker(s): Albert Ai (University of Wisconsin-Madison)
Location: MSRI: Online/Virtual
  • partial differential equations

  • water waves

  • fluids

  • Microlocal analysis

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Two Dimensional Gravity Water Waves at Low Regularity


In this talk, we will consider the low regularity well-posedness problem for the two dimensional gravity water waves. This quasilinear dispersive system admits an interesting structure which we exploit to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier energy estimates of Hunter-Ifrim-Tataru. These results allow us to significantly lower the regularity threshold for local well-posedness, even without using dispersive properties. Combined with nonlinear vector field Sobolev inequalities, an idea first introduced by the last two authors in the context of the Benjamin-Ono equations, these improvements extend to global solutions for small and localized data. This is joint work with Mihaela Ifrim and Daniel Tataru.

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Two Dimensional Gravity Water Waves at Low Regularity

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