4.3 Article

Dynamics of threshold solutions for energy critical NLW with inverse square potential

Related references

Note: Only part of the references are listed.
Article Mathematics

Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs

Zhiwu Lin et al.

Summary: In this paper, we study the properties of general linear Hamiltonian systems in a Hilbert space. By structural decomposition, we prove the linear exponential trichotomy and an instability index theorem for the system, and provide index information for pure imaginary eigenvalues. Moreover, we discuss several specific Hamiltonian PDEs, including dispersive long wave models, the 2D Euler equation for ideal fluids, and the 2D nonlinear Schrödinger equation with nonzero conditions at infinity.

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY (2022)

Article Mathematics, Applied

DYNAMICS OF THRESHOLD SOLUTIONS FOR ENERGY CRITICAL NLS WITH INVERSE SQUARE POTENTIAL

Kai Yang et al.

Summary: This article examines the focusing energy critical nonlinear Schrodinger equation with inverse square potential in dimensions 3, 4, and 5. The characteristics of solutions on the energy surface of the ground state are described and proved. It is shown that solutions with kinetic energy less than that of the ground state must converge to the ground state, while solutions with greater kinetic energy will blow up in finite time.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2022)

Article Mathematics

Strichartz estimates and wave equation in a conic singular space

Junyong Zhang et al.

MATHEMATISCHE ANNALEN (2020)

Article Mathematics, Applied

The energy-critical nonlinear wave equation with an inverse-square potential

Changxing Miao et al.

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE (2020)

Article Mathematics

Sobolev spaces adapted to the Schrodinger operator with inverse-square potential

R. Killip et al.

MATHEMATISCHE ZEITSCHRIFT (2018)

Article Physics, Mathematical

Invariant Manifolds of Traveling Waves of the 3D Gross-Pitaevskii Equation in the Energy Space

Jiayin Jin et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2018)

Article Mathematics, Applied

THE ENERGY-CRITICAL NLS WITH INVERSE-SQUARE POTENTIAL

Rowan Killip et al.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2017)

Article Mathematics

DYNAMICS FOR THE ENERGY CRITICAL NONLINEAR WAVE EQUATION IN HIGH DIMENSIONS

Dong Li et al.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2011)

Article Mathematics

Dynamics for the energy critical nonlinear Schrodinger equation in high dimensions

Dong Li et al.

JOURNAL OF FUNCTIONAL ANALYSIS (2009)