Yonggeun Cho

SOBOLEV INEQUALITIES WITH SYMMETRY

In this paper, we derive some Sobolev inequalities for radially symmetric functions in Ḣs with 1/2 < s < n/2. We show the end point case s = 1/2 on the homogeneous Besov space . These results are extensions of the well-known Strauss inequality [13]. Also non-radial extensions are given, which show that compact embeddings are possible in some Lp spaces if a suitable angular regularity is imposed.

Mixed Norm Estimates of Schrödinger Waves and Their Applications

In this paper we establish mixed norm estimates of interactive Schrödinger waves and apply them to study smoothing properties and global well-posedness of the nonlinear Schrödinger equations with mass critical nonlinearity.

Finite time blowup for the fourth-order NLS

We consider the fourth-order Schrodinger equation with fo- cusing inhomogeneous nonlinearity (−|x| −2 |u| 4 n u) in high space dimen- sions. Extending Glasseys virial argument, we show the finite time blow- up of solutions when the energy is negative.

Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity

This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrodinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method.