• Title/Summary/Keyword: U-Space

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THE NAVIER-STOKES EQUATIONS WITH INITIAL VALUES IN BESOV SPACES OF TYPE B-1+3/qq,∞

  • Farwig, Reinhard;Giga, Yoshikazu;Hsu, Pen-Yuan
    • Journal of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1483-1504
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    • 2017

  • 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.

  • https://doi.org/10.4134/JKMS.j160529 인용 PDF KSCI

A Study on U-Service for Security in U-City Newtown Planning (신도시계획의 계획지표를 반영한 U-City의 U-방범서비스 개선방안 연구)

  • Yoon, Hyo Jin
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.5D
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    • pp.645-654
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    • 2009

  • This study started with necessity of historical spatial planning skills in U-city planning. Though U-city technology and information are very important, U-city development should be considered on the base of various experience of spatial planning. This study explored spatial planning indexes change in the recent newtown plans. In particular, safety and security were intensively analyzed. In addition, many theories on safe urban space, ubiquitous technology, traditional defensible space, and CPTED (Crime Prevention through Environmental Design) are compared. The findings are as follows. First, each planning is not integrated and there is lack of network among each planning. Specifically, from the crime prevention perspective, there is only mechanical monitoring such as CCTV without architectural approach. Even though CCTV is social needs, it is necessary to adopt it with architectural environment in order to improve the synergy effect of spatial planning and non-spatial planning.

  • https://doi.org/10.12652/Ksce.2009.29.5D.645 인용 PDF

On real hypersurfaces of a complex hyperbolic space

  • Kang, Eun-Hee;Ki, U-Hang
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.173-184
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    • 1997

  • An n-dimensional complex space form $M_n(c)$ is a Kaehlerian manifold of constant holomorphic sectional curvature c. As is well known, complete and simply connected complex space forms are a complex projective space $P_n C$, a complex Euclidean space $C_n$ or a complex hyperbolic space $H_n C$ according as c > 0, c = 0 or c < 0.

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Totally real submanifolds with parallel mean curvature vector in a complex space form

  • Ki, U-Hang;Kim, Byung-Hak;Kim, He-Jin
    • Journal of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.835-848
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    • 1995

  • Let $M_n$(c) be an n-dimensional complete and simply connected Kahlerian manifold of constant holomorphic sectional curvature c, which is called a complex space form. Then according to c > 0, c = 0 or c < 0 it is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$.

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Characterizations of some real hypersurfaces in a complex space form in terms of lie derivative

  • Ki, U-Hang;Suh, Young-Jin
    • Journal of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.161-170
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    • 1995

  • A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. Takagi [12] and Berndt [2] classified all homogeneous real hypersufaces of $P_nC$ and $H_nC$.

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