Advanced Mathematical Physics Problems
Description: This cluster of papers focuses on the global well-posedness, scattering, and blow-up phenomena for various nonlinear wave equations, including the nonlinear Schrödinger equation, wave maps equation, Korteweg-de Vries equation, and dispersive equations. The research also explores the behavior of solitons and critical exponent for energy-critical equations.
Characteristic keywords: nonlinear Schrödinger equation, nonlinear dispersive equations, local well-posedness, nonlinear wave equations, global well-posedness, Strichartz estimates, dispersive equations, finite-time blow-up, semilinear wave equation, blow-up solutions, small initial data, nonlinear Klein-Gordon equation, power nonlinearity, cubic nonlinear Schrödinger equation, dispersive estimates, energy space, critical Sobolev spaces, quasilinear wave equations, focusing nonlinear Schrödinger equation, low regularity solutions, Benjamin-Ono equation, derivative nonlinear Schrödinger equation, generalized Korteweg-de Vries equation, blow-up rate, focusing nonlinearity
Sibling topics: Mathematical Dynamics and Fractals, Homotopy and Cohomology in Algebraic Topology, Advanced Operator Algebra Research, Spectral Theory in Mathematical Physics, Stochastic processes and statistical mechanics, Numerical methods in inverse problems, Advanced Banach Space Theory, Advanced Algebra and Geometry, advanced mathematical theories, Mathematical and Theoretical Analysis, Advanced Mathematical Theories
Parent subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
OpenAlex ID: T11654