The 3D energy-critical inhomogeneous nonlinear Schrodinger equation with strong singularity

2025/01/06 by Lee, Yoonjung
#35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35A01 #Secondary: 35B45

paper · doi:10.48550/arxiv.2501.02697

Abstract

In this paper, we study the Cauchy problem for the 3D energy-critical inhomogeneous nonlinear Schrödinger equation(INLS) i∂_tu+Δu=±|x|^-α|u|^4-2αu with strong singularity 3/2≤ α<2. The well-posedness problem is well-understood for 0<α<3/2, but the case 3/2≤ α<2 has remained open so far. We address the local/small data global well-posedness result for 3/2≤ α<11/6 by improving the inhomogeneous Strichartz estimates on the weighted space.

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