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RISS 인기검색어
- 검색키워드
- 저자 : Pen-Yuan Hsu (검색결과 3 건)
- 무료
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Farwig, Reinhard,Giga, Yoshikazu,Hsu, Pen-Yuan Korean Mathematical Society 2017 대한수학회지 Vol.54 No.5
We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain ${\Omega}{\subset}{\mathbb{R}}^3$ with initial value $u_0{\in}L^2_{\sigma}({\Omega})$. It is known that a weak solution is a local strong solution in the sense of Serrin if $u_0$ satisfies the optimal initial value condition $u_0{\in}B^{-1+3/q}_{q,s_q}$ with Serrin exponents $s_q$ > 2, q > 3 such that ${\frac{2}{s_q}}+{\frac{3}{q}}=1$. This result has recently been generalized by the authors to weighted Serrin conditions such that u is contained in the weighted Serrin class ${{\int}_0^T}({\tau}^{\alpha}{\parallel}u({\tau}){\parallel}_q)^s$ $d{\tau}$ < ${\infty}$ with ${\frac{2}{s}}+{\frac{3}{q}}=1-2{\alpha}$, 0 < ${\alpha}$ < ${\frac{1}{2}}$. This regularity is guaranteed if and only if $u_0$ is contained in the Besov space $B^{-1+3/q}_{q,s}$. In this article we consider the limit case of initial values in the Besov space $B^{-1+3/q}_{q,{\infty}}$ and in its subspace ${{\circ}\atop{B}}^{-1+3/q}_{q,{\infty}}$ based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.
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THE NAVIER-STOKES EQUATIONS WITH INITIAL VALUES IN BESOV SPACES OF TYPE B-1q,∞+3/q
Reinhard Farwig,Yoshikazu Giga,Pen-Yuan Hsu 대한수학회 2017 대한수학회지 Vol.54 No.5
We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain $\Om \subset {\mathbb R}^3$ with initial value $u_0\in L^{2}_{\sigma}(\Om)$. It is known that a weak solution is a local strong solution in the sense of Serrin if $u_0$ satisfies the optimal initial value condition $u_0\in B^{-1+3/q}_{q,s_q}$ with Serrin exponents $s_q>2, q>3$ such that $\frac2{s_q} + \frac3q =1$. This result has recently been generalized by the authors to weighted Serrin conditions such that $u$ is contained in the weighted Serrin class $\int_0^T (\tau^\alpha \|u(\tau)\|_q)^s\dd\tau<\infty$ with $\frac{2}{s} + \frac{3}{q} =1-2\alpha$, $0<\alpha<\frac12$. This regularity is guaranteed if and only if $u_0$ is contained in the Besov space $B^{-1+3/q}_{q,s}$. In this article we consider the limit case of initial values in the Besov space $B^{-1+3/q}_{q,\infty}$ and in its subspace ${\stackrel{\circ}{B}}{}^{-1+3/q}_{q,\infty}$ based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.
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Family History of Cancer and Head and Neck Cancer Risk in a Chinese Population
Huang, Yu-Hui Jenny,Lee, Yuan-Chin Amy,Li, Qian,Chen, Chien-Jen,Hsu, Wan-Lun,Lou, Pen-Jen,Zhu, Cairong,Pan, Jian,Shen, Hongbing,Ma, Hongxia,Cai, Lin,He, Baochang,Wang, Yu,Zhou, Xiaoyan,Ji, Qinghai,Zho Asian Pacific Journal of Cancer Prevention 2015 Asian Pacific journal of cancer prevention Vol.16 No.17
Background: The aim of this study was to investigate whether family history of cancer is associated with head and neck cancer risk in a Chinese population. Materials and Methods: This case-control study included 921 cases and 806 controls. Recruitment was from December 2010 to January 2015 in eight centers in East Asia. Controls were matched to cases with reference to sex, 5-year age group, ethnicity, and residence area at each of the centers. Results: We observed an increased risk of head and neck cancer due to first degree family history of head and neck cancer, but after adjustment for tobacco smoking, alcohol drinking and betel quid chewing the association was no longer apparent. The adjusted OR were 1.10 (95% CI=0.80-1.50) for family history of tobacco-related cancer and 0.96 (95%CI=0.75-1.24) for family history of any cancer with adjustment for tobacco, betel quid and alcohol habits. The ORs for having a first-degree relative with HNC were higher in all tobacco/alcohol subgroups. Conclusions: We did not observe a strong association between family history of head and neck cancer and head and neck cancer risk after taking into account lifestyle factors. Our study suggests that an increased risk due to family history of head and neck cancer may be due to shared risk factors. Further studies may be needed to assess the lifestyle factors of the relatives.
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