Department of Mathematics

Analysis and PDE

  •  Michael McNulty, UC Riverside
  •  On the Stability of Self-Similar Blow-Up for Nonlinear Wave Equations
  •  02/02/2022
  •  4:10 PM - 5:00 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Willie Wai-Yeung Wong (wongwil2@msu.edu)

Of fundamental importance to the study of nonlinear wave equations is the well-posedness of the associated Cauchy problem. While some equations may admit solutions that exist for all time, some equations admit solutions which blow up in finite time. Self-similar solutions provide examples of solutions which are initially smooth and compactly supported yet fail to be continuously differentiable after a finite amount of time. In this talk, we will review developments in the study of stable self-similar blow-up for nonlinear wave equations. After reviewing what is known for a variety of such equations, we will introduce the strong-field Skyrme model. This model is a particular limiting case of the Skyrme model, a quasilinear modification of the nonlinear sigma model (wave maps). We will present recent progress toward establishing the stability of an explicit self-similar solution of the strong-field Skyrme model’s equation of motion. In particular, we will emphasize new challenges due to nonlinear structures absent in previously studied equations.

 

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