Nonlinear Wave Equations

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The aim of the proposed work is to study the behavior of low regularity solutions to nonlinear wave equations. This problem is by now well understood for generic equations. However, most nonlinear wave equations arising in physics (e.g., Einstein's equations in general relativity) exhibit some kind of special structure which, one expects, guarantees a much better behavior of solutions than for a generic equation. It is precisely this type of equations that the proposed research will focus on. This subject is largely unexplored, and, until now, was considered to be out of reach. However, recent work of the PI may hold the key to progress in this field.