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Navier-Stokes equations with anisotropic regularity in one velocity component

Zujin Zhang|Xiqin Ouyang|Xian Yang
장전수학회 (Jangjeon Mathematical Society)|2016.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제19권 제3호|pp. 465-476|DOI 10.17777/pjms.2016.19.3.003

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키워드

regularity criteriaNavier-Stokes equations
주제분류수학

초록

In 2003, Escauriaza, Seregin, Sverak showed that if u ∈ L∞(0, T;L3(R³)), then the solution is smooth on (0,T). In this paper, we shall derive the corresponding result for the one component case, that is, we obtain the following regularity criterion: u3 ∈ L∞(0,T;L2 15/4 L3 10/3 L13(R³)) or υ3 ∈ L∞(0,T;L1 15/4 L3 10/3 L23(R³)).

Abstract

In 2003, Escauriaza, Seregin, Sverak showed that if u ∈ L∞(0, T;L3(R³)), then the solution is smooth on (0,T). In this paper, we shall derive the corresponding result for the one component case, that is, we obtain the following regularity criterion: u3 ∈ L∞(0,T;L2 15/4 L3 10/3 L13(R³)) or υ3 ∈ L∞(0,T;L1 15/4 L3 10/3 L23(R³)).

참고문헌 (40)

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