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 for . For any prescribed finite se…
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 amplificatio…
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…