Remarks on the Global Existence for Incompressible Navier-Stokes Equations

Citation:

Sheng WANG,Zexian ZHANG,Yi ZHOU.Remarks on the Global Existence for Incompressible Navier-Stokes Equations[J].Chinese Annals of Mathematics B,2024,45(4):529~536
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Authors:

Sheng WANG; Zexian ZHANG;Yi ZHOU

Foundation:

the National Natural Science Foundation of China (No. 12171097), the Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), the Ministry of Education of China, Shanghai Key Laboratory for Contemporary Applied Mathematics and Shanghai Science and Technology Program (No. 21JC1400600).
Abstract: In this article, the authors use the special structure of helicity for the threedimensional incompressible Navier-Stokes equations to construct a family of finite energy smooth solutions to the Navier-Stokes equations which critical norms can be arbitrarily large.

Keywords:

Navier-Stokes euqations, Helicity, Global existence, Critical norm

Classification:

17B40, 17B50
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