On Critical Cases of Sobolev′s Inequalities
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In this article, a new form of the Trudinger-type inequality, which shows an explicit dependence, is presented, and an alternative proof of the Brezis-Gallouet-Wainger inequality is given.About:
This article is published in Journal of Functional Analysis.The article was published on 1995-02-01 and is currently open access. It has received 200 citations till now. The article focuses on the topics: Sobolev inequality & Kantorovich inequality.read more
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The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
TL;DR: In this article, the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda were studied.
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Trudinger type inequalities in ^{} and their best exponents
Shinji Adachi,Kazunaga Tanaka +1 more
TL;DR: In this article, the limit case of Sobolev's inequalities was studied in RN and the best exponents αN were shown to be false for all α ∈ (0, αN), αN = Nω N−1 (ωN−1 is the surface area of the unit sphere in RN ), and αN is defined by exp(ξ) − N−2 ∑ j=0 1 j! ξ.
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Limiting case of the Sobolev inequality in BMO, with application to the Euler equations
Hideo Kozono,Yasushi Taniuchi +1 more
TL;DR: In this paper, a logarithmic Sobolev inequality by means of the BMO-norm in the critical exponents of the Euler equation was proved, and a blow-up criterion of solutions to Euler equations was established.
Trudinger type inequalities in R^N and their best exponents
Shinji Adachi,Kazunaga Tanaka +1 more
TL;DR: In this paper, the limit case of Sobolev's inequalities was studied in RN and the best exponents αN were shown to be false for all α ∈ (0, αN), αN = Nω N−1 (ωN−1 is the surface area of the unit sphere in RN ), and αN is defined by exp(ξ) − N−2 ∑ j=0 1 j! ξ.
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Global strong solution to the 2D nonhomogeneous incompressible MHD system
TL;DR: In this article, the authors proved the global existence of strong solution with vacuum to the 2D nonhomogeneous incompressible Navier-Stokes equations, as long as the initial data satisfies some compatibility condition.