http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
- 中文 을 입력하시려면 zhongwen을 입력하시고 space를누르시면됩니다.
- 北京 을 입력하시려면 beijing을 입력하시고 space를 누르시면 됩니다.
RISS 인기검색어
- 검색키워드
- 저자 : Yoshikazu Giga (검색결과 2 건)
- 무료
- 기관 내 무료
- 유료
-
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.
-
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.
연관 검색어 추천
이 검색어로 많이 본 자료
활용도 높은 자료
