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Explore the formation of singularities and quasi-singularities in partial differential equations through this 53-minute conference talk. Examine how smooth forcing terms can generate solutions with quasi-singularities in fundamental models including the nonlinear Schrödinger equation and shallow water equation. Discover how well-localized smooth forcing in Fourier space produces solutions with power law-decaying Fourier spectra that depend on the algebraic structure of the equation's nonlinearity. Analyze the stability properties of these solutions and observe numerical demonstrations of the phenomena. Learn about collaborative research findings from work conducted with R. Carles (CNRS), L. Martaud, and G. Beck (INRIA) that advances understanding of how smooth coefficients and forcing can lead to complex solution behaviors in PDEs.
