Department of Mathematics

Analysis and PDE

  •  Michael McNulty, MSU
  •  Conditionally Stable Self-Similar Blowup for the Supercritical Quadratic Wave Equation Beyond the Light Cone
  •  09/21/2022
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall
  •  Willie Wai-Yeung Wong (

Nonlinear wave equations of power-type serve as excellent toy models for geometric PDEs such as the Yang-Mills and wave maps equations. Of great interest in the energy supercritical setting is that of threshold phenomena. In this setting, unstable self-similar blowup solutions are believed to play an essential role in describing the threshold of singularity formation. We will discuss the stability of an explicitly known, unstable self-similar blowup solution of the energy supercritical quadratic wave equation in a region of spacetime which extends beyond the time of blowup. To overcome this instability, we introduce a new canonical method to investigate unstable self-similar solutions. This work represents the first steps toward an understanding of threshold phenomena in the energy supercritical setting.



Department of Mathematics
Michigan State University
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