arXiv subjects

Pang-Hung Chung

Publications and source records attributed to Pang-Hung Chung.

4 recordsLinked to original sources

arXiv2026

Scattering Criteria for the Three-Dimensional Focusing Energy-Critical Generalized Hartree Equation

Two nonradial scattering criteria are established for the three-dimensional focusing energy-critical generalized Hartree equation below the ground-state threshold, under a bounded-scale concentration--compactness reduction. The first criterion is formulated in terms of fixed-center occupation windows and quantitative bounds on the motion of the concentration center. The second is based on uniform low-frequency $L^2$-decay, which yields finite mass, precompactness in the inhomogeneous energy space, a zero-momentum normalization, and sublinear center drift. The proofs combine a localized Hartree virial identity with a critical Hardy--Littlewood--Sobolev estimate controlling the nonlocal tail.

math.AP↗

arXiv2026

Finite-mass soliton-type rigidity and four-channel reduction for the three-dimensional nonradial focusing energy-critical nonlinear Schrödinger equation

The concentration--compactness channels below the ground-state threshold are investigated for the three-dimensional nonradial focusing energy-critical nonlinear Schrödinger equation. After one-sided normalization, a minimal critical element falls into four classes: the finite-time, rapid-cascade, bounded-scale finite-mass, and residual quasi-soliton channels. The first three classes are rigorously excluded. The main result shows, without radial symmetry, zero momentum, or a slow spatial center, that every finite-mass bounded-scale almost-periodic solution is identically zero. Consequently, any minimal counterexample to below-threshold scattering must lie in the residual quasi-soliton channel; if its scale is bounded, then it has infinite mass at every time.

math.AP↗

arXiv2026

Scattering and Low-Speed Critical Elements for the 3D Focusing Energy-Critical NLS

The below-threshold scattering problem is considered for the three-dimensional focusing energy-critical nonlinear Schrödinger equation. A main non-radial obstruction is the possible drift of the concentration center of a soliton-like critical element, which prevents a fixed-center localized virial estimate from closing directly. It is shown that such a compact critical solution must vanish if it has an $L_t^\infty L_x^q$ bound and its center drifts sufficiently slowly. The result covers the pure-energy, endpoint $L^4$, and finite-mass regimes and gives a corresponding conditional scattering criterion.

math.AP↗

arXiv2026

Conditional scattering criteria for cylindrical threshold dynamics of the three-dimensional focusing energy-critical Schrödinger equation

Below-threshold scattering is studied for the three-dimensional focusing energy-critical Schrödinger equation in the cylindrically symmetric class. For soliton-like compact critical elements, two linked rigidity entrances are isolated: a best fixed-axis window condition for the axial center and a low-frequency tail smallness condition. A shifted localized virial estimate and a finite-mass virial argument after axial zero-momentum normalization exclude these entrances, yielding a conditional cylindrical threshold scattering criterion via compactness reduction.

math.AP↗