Bilinear Strichartz's type estimates in Besov spaces with application to inhomogeneous nonlinear biharmonic Schrödinger equation

Abstract

In this paper, we consider the well-posedness of the inhomogeneous nonlinear biharmonic Schrödinger equation with spatial inhomogeneity coefficient $K(x)$ behaves like ${\left|x\right|}^{-b}$ for $0<b<\min \left\{\frac{N}{2},4\right\}$. We show the local well-posedness in the whole $H^s$-subcritical case, with $0<s\le 2$. The difficulties of this problem come from the singularity of $K(x)$ and the lack of differentiability of the nonlinear term. To resolve this, we derive the bilinear Strichartz's type estimates for the nonlinear biharmonic Schrödinger equations in Besov spaces.

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Cited by in corpus (1)

• Scattering for a class of non-radial inhomogeneous bi-harmonic Hartree equations