Dynamics of nonlinear wave equations

Abstract

In this lecture, we will survey the study of dynamics of the nonlinear wave equation in recent years. We refer to some lecture notes including such as C. Kenig \cite{Kenig01,Kenig02}, C. Kenig and F. Merle \cite{KM1} J. Shatah and M. Struwe \cite{SS98}, and C. Sogge \cite{sogge:wave} etc. This lecture was written for LIASFMA School and Workshop on Harmonic Analysis and Wave Equations in Fudan universty.

arXiv comment80pages. This lecture was written for LIASFMA School on Harmonic Analysis and Wave Equations in Fudan universty(2017). arXiv admin note: text overlap with arXiv:1506.00788, arXiv:0710.5934, arXiv:1407.4525, arXiv:1601.01871, arXiv:1301.4835, 1509.03331, arXiv:1010.3799, arXiv:1201.3258, arXiv:0911.4534, arXiv:1411.7905, by other authors

References in corpus (10)

• Weak-strong uniqueness for the isentropic compressible Navier-Stokes system
• Ill-posedness for nonlinear Schrodinger and wave equations
• On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations
• Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5
• Maximizers for the Strichartz Inequalities for the Wave Equation
• Scattering for the radial 3d cubic wave equation
• Scattering for radial, semi-linear, super-critical wave equations with bounded critical norm
• Global well-posedness and scattering for the radial, defocusing, cubic wave equation with almost sharp initial data
• Blow-up results for semilinear wave equations in the super-conformal case
• Nonexistence of radial two-bubbles with opposite signs for the energy-critical wave equation