The cubic-quintic nonlinear Schrödinger equation with inverse-square potential

DOI10.1007/s00030-024-00979-8zbMATH Open1547.35616MaRDI QIDQ6606857

Alex H. Ardila, Jason Murphy

Publication date: 17 September 2024

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

zbMATH Keywords

scatteringsolitoninverse-square potentialcubic-quintic NLS

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• The energy-critical NLS with inverse-square potential
• Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on \({\mathbb{R}^3}\)
• On the Cauchy problem of 3D energy-critical Schrödinger equations with subcritical perturbations
• Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
• Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential
• Scattering in \(H^{1}\) for the intercritical NLS with an inverse-square potential
• Sobolev spaces adapted to the Schrödinger operator with inverse-square potential
• Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential
• \(L^2\) concentration of blow-up solutions for the mass-critical NLS with inverse-square potential
• The energy-critical nonlinear wave equation with an inverse-square potential
• Scattering of the energy-critical NLS with inverse square potential
• The focusing cubic NLS with inverse-square potential in three space dimensions.
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Scattering of the focusing energy-critical NLS with inverse square potential in the radial case
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• Scattering for the Cubic-Quintic NLS: Crossing the Virial Threshold

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