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| An Attempt at Axiomatization of Extending Mechanism of Solutionsto the Fluid Dynamical Systems |
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Citation： |
Jinkai LI,Meng WANG,Wendong WANG.An Attempt at Axiomatization of Extending Mechanism of Solutionsto the Fluid Dynamical Systems[J].Chinese Annals of Mathematics B,2024,45(6):957~970 |
| Page view： 786
Net amount： 262 |
Authors： |
Jinkai LI; Meng WANG;Wendong WANG |
Foundation： |
the National Natural Science Foundation of China (Nos. 12371204,
12371100, 12071054), the Key Project of National Natural Science Foundation of China (No. 12131010)
and the National Support Program for Young Top-Notch Talents and Dalian High-level Talent Innovation Project (No. 2020RD09). |
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| Abstract： |
Note that some classic fluid dynamical systems such as the Navier-Stokes
equations, Magnetohydrodynamics (MHD for short), Boussinesq equations and etc., are
observably different from each other but obey some energy inequalities of the similar type.
In this paper, the authors attempt to axiomatize the extending mechanism of solutions to
these systems, merely starting from several basic axiomatized conditions such as the local
existence, joint property of solutions and some energy inequalities. The results established
have nothing to do with the concrete forms of the systems and, thus, give the extending
mechanisms in a unified way to all systems obeying the axiomatized conditions. The key
tools are several new multiplicative interpolation inequalities of Besov type, which have
their own interests. |
Keywords： |
Interpolation inequalities of Besov type, Blow-up criteria, Navier-Stokes
equations |
Classification： |
35Q30, 76D03 |
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