3 papers
math.AP2026
Formation of quasi-singularities of shock and implosion type for compressible Euler flows
Xieling Fan, Hongyu Liu
This paper investigates a novel quasi-singularity formation phenomenon in the isentropic compressible Euler equations in three dimensions. For any prescribed finite set of points $…
math.AP2026
Construction of Solutions with Extraordinary Gradient Amplification and Localization for Schrödinger Equations
Huaian Diao, Xieling Fan, Hongyu Liu
This paper constructs solutions to linear and nonlinear Schrödinger-type equations in two and three spatial dimensions that exhibit prescribed, extraordinary gradient amplification…
math.AP2025
A New Quasi-Singularity Formation Mechanism for Second-order Hyperbolic Equations
Huaian Diao, Xieling Fan, Hongyu Liu
This paper investigates a novel mechanism for quasi-singularity formation in both linear and nonlinear hyperbolic wave equations in two and three dimensions. We prove that over any…