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Remarks on the pressure regularity criterion of the micropolar fluid equations in multiplier spaces. (English) Zbl 1257.35149

Summary: This study is devoted to investigating the regularity criterion of weak solutions of the micropolar fluid equations in \(\mathbb R^3\). The weak solution of micropolar fluid equations is proved to be smooth on \((0, T]\) when the pressure \(\pi(x, t)\) satisfies the following growth condition in the multiplier spaces \(\dot{X}^r, \int^T_0 ||\pi(s, \cdot)||^{2/(2-r)}_{\dot{X}^r} / (1 + \ln(e + ||\pi(s, \cdot)||_{L^2})), ds < \infty\), and \(0 \leq r \leq 1\). The previous results on Lorentz spaces and Morrey spaces are obviously improved.

MSC:

35Q35 PDEs in connection with fluid mechanics
35D30 Weak solutions to PDEs
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35B65 Smoothness and regularity of solutions to PDEs
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