arXiv subjects

Youngwoo Koh

Publications and source records attributed to Youngwoo Koh.

22 records · Page 2Linked to original sources

arXiv2016

Weak solutions for one-dimensional non-convex elastodynamics

We explore local existence and properties of classical weak solutions to the initial-boundary value problem of a one-dimensional quasilinear equation of elastodynamics with non-convex stored-energy function, a model of phase transitions in elastic bars proposed by Ericksen [19]. The instantaneous formation of microstructures of local weak solutions is observed for all smooth initial data with initial strain having its range overlapping with the phase transition zone of the Piola-Kirchhoff stress. As byproducts, it is shown that such a problem admits a local weak solution for all smooth initial data and local weak solutions that are smooth for a short period of time and exhibit microstructures thereafter for some smooth initial data. In a parallel way, we also include some results concerning one-dimensional quasilinear hyperbolic-elliptic equations.

math.AP↗

arXiv2015

On weighted $L^2$ estimates for solutions of the wave equation

In this paper we consider weighted $L^2$ integrability for solutions of the wave equation. For this, we obtain some weighed $L^2$ estimates for the solutions with weights in Morrey-Campanato classes. Our method is based on a combination of bilinear interpolation and localization argument which makes use of Littlewood-Paley theorem and a property of Hardy-Littlewood maximal functions. We also apply the estimates to the problem of well-posedness for wave equations with potentials.

math.AP↗

arXiv2015

On inhomogeneous Strichartz estimates for fractional Schrödinger equations and their applications

In this paper we obtain some new inhomogeneous Strichartz estimates for the fractional Schrödinger equation in the radial case. Then we apply them to the well-posedness theory for the equation $i\partial_{t}u+|\nabla|^αu=V(x,t)u$, $1<α<2$, with radial $\dot{H}^γ$ initial data below $L^2$ and radial potentials $V\in L_t^rL_x^w$ under the scaling-critical range $α/r+n/w=α$.

math.AP↗

arXiv2015

Global well-posedness for higher-order Schrödinger equations in weighted $L^2$ spaces

We obtain the global well-posedness for Schrödinger equations of higher orders in weighted $L^2$ spaces. This is based on weighted $L^2$ Strichartz estimates for the corresponding propagator with higher-order dispersion. Our method is also applied to the Airy equation which is the linear component of Korteweg-de Vries type equations.

math.AP↗