http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
FINITE TIME BLOWUP FOR THE FOURTH-ORDER NLS
Cho, Yonggeun,Ozawa, Tohru,Wang, Chengbo Korean Mathematical Society 2016 대한수학회보 Vol.53 No.2
We consider the fourth-order $Schr{\ddot{o}}dinger$ equation with focusing inhomogeneous nonlinearity ($-{\mid}x{\mid}^{-2}{\mid}u{\mid}^{\frac{4}{n}}u$) in high space dimensions. Extending Glassey's virial argument, we show the finite time blowup of solutions when the energy is negative.
On the orbital stability of fractional Schrödinger equations
Cho, Yonggeun,Hajaiej, Hichem,Hwang, Gyeongha,Ozawa, Tohru American Institute of Mathematical Sciences 2014 COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Vol.13 No.3
We show the existence of ground state and orbital stability of standing waves of fractional Schrodinger equations with power type nonlinearity. For this purpose we establish the uniqueness of weak solutions.
Concordance of Three Automated Procalcitonin Immunoassays at Medical Decision Points
Cho Hae Weon,Kim Sun Hee,Cho Yonggeun,Jeong Seok Hoon,Lee Sang-Guk 대한진단검사의학회 2021 Annals of Laboratory Medicine Vol.41 No.4
Procalcitonin (PCT) is a useful bacterial infection biomarker with the potential for guiding antibiotic therapy. We evaluated the concordance of three automated PCT immunoassays: Kryptor (BRAHMS GmbH, Hennigsdorf, Germany), Atellica IM 1600 (Siemens Healthcare Diagnostics, Munich, Germany), and Cobas e801 (Roche Diagnostics, Mannheim, Germany). In 119 serum samples with a PCT concentration <5.00 μg/L, Kryptor (reference assay) was compared with the other two immunoassays by Spearman’s rank correlation, regression analysis, and concordance at two antibiotic stewardship medical decision points: 0.25 and 0.50 μg/L. The Atellica IM 1600 and Cobas e801 results showed high correlations with those of Kryptor, with correlation coefficient (ρ) values of 0.97 and 0.99, respectively. However, negative biases were observed in both immunoassays (slope/y-intercept: 0.75/–0.00 for Atellica IM 1600; 0.88/–0.01 for Cobas e801). Atellica IM 1600 and Cobas e801 demonstrated excellent concordance with Kryptor at both medical decision points, with linearly weighted κ values of 0.90 and 0.92, respectively, despite discrepancies, which were more prominent at the 0.25 μg/L medical decision point. Based on these biases and discrepancies, the alternate use of different PCT immunoassays in repeat examinations is inadvisable. Standardization is required before comparing the results of different PCT immunoassays.
SMALL DATA SCATTERING OF HARTREE TYPE FRACTIONAL SCHRÖDINGER EQUATIONS IN DIMENSION 2 AND 3
Cho, Yonggeun,Ozawa, Tohru Korean Mathematical Society 2018 대한수학회지 Vol.55 No.2
In this paper we study the small-data scattering of the d dimensional fractional $Schr{\ddot{o}}dinger$ equations with d = 2, 3, $L{\acute{e}}vy$ index 1 < ${\alpha}$ < 2 and Hartree type nonlinearity $F(u)={\mu}({\mid}x{\mid}^{-{\gamma}}{\ast}{\mid}u{\mid}^2)u$ with max(${\alpha}$, ${\frac{2d}{2d-1}}$) < ${\gamma}{\leq}2$, ${\gamma}$ < d. This equation is scaling-critical in ${\dot{H}}^{s_c}$, $s_c={\frac{{\gamma}-{\alpha}}{2}}$. We show that the solution scatters in $H^{s,1}$ for any s > $s_c$, where $H^{s,1}$ is a space of Sobolev type taking in angular regularity with norm defined by ${\parallel}{\varphi}{\parallel}_{H^{s,1}}={\parallel}{\varphi}{\parallel}_{H^s}+{\parallel}{\nabla}_{{\mathbb{S}}{\varphi}}{\parallel}_{H^s}$. For this purpose we use the recently developed Strichartz estimate which is $L^2$-averaged on the unit sphere ${\mathbb{S}}^{d-1}$ and utilize $U^p-V^p$ space argument.
Finite time blowup for the fourth-order NLS
Yonggeun Cho,Tohru Ozawa,Chengbo Wang 대한수학회 2016 대한수학회보 Vol.53 No.2
We consider the fourth-order Schr\"odinger equation with focusing inhomogeneous nonlinearity $(-|x|^{-2}|u|^\frac4n u)$ in high space dimensions. Extending Glassey's virial argument, we show the finite time blow-up of solutions when the energy is negative.
Existence results for viscous polytropic fluids with vacuum
Cho, Yonggeun,Kim, Hyunseok Elsevier 2006 Journal of differential equations Vol.228 No.2
<P><B>Abstract</B></P><P>We consider the full Navier–Stokes equations for viscous polytropic fluids with nonnegative thermal conductivity. We prove the existence of unique local strong solutions for all initial data satisfying some compatibility condition. The initial density need not be positive and may vanish in an open set. Moreover our results hold for both bounded and unbounded domains.</P>
ON THE ORBITAL STABILITY OF INHOMOGENEOUS NONLINEAR SCHRÖDINGER EQUATIONS WITH SINGULAR POTENTIAL
Cho, Yonggeun,Lee, Misung Korean Mathematical Society 2019 대한수학회보 Vol.56 No.6
We show the existence of ground state and orbital stability of standing waves of nonlinear $Schr{\ddot{o}}dinger$ equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.