Scattering for the non-radial inhomogenous biharmonic NLS equation

Author(s)

Campos, Luccas ; Guzman, Carlos M.

• Document type: Journal article
• Source: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 61, n. 4, p. 15-pg., 2022-08-01.

Abstract

We consider the focusing inhomogeneous biharmonic nonlinear Schrodinger equation in H-2(R-N), iu(t) + Delta(2)u - vertical bar x vertical bar(-b) vertical bar u vertical bar(alpha) u = 0, when b > 0 and N >= 5. We first obtain a small data global result in H-2, which, in the five-dimensional case, improves a previous result from Pastor and the second author. In the sequel, weshowthemain result, scattering below the mass-energy threshold in the intercritical case, that is, 8-2b/N < alpha < 8-2b/N-4, without assuming radiality of the initial data. The proof combines the decay of the nonlinearity with Virial-Morawetz-type estimates to avoid the radial assumption, allowing for a much simpler proof than the Kenig-Merle roadmap. (AU)

• FAPESP's process: 20/10185-1 - Local and global behaviour of solutions of dispersive equations
• Grantee: Luccas Cassimiro Campos
• Support Opportunities: Scholarships in Brazil - Post-Doctoral