Global Well-Posedness in the Critical Besov Spaces for the Incompressible Oldroyd-B Model Without Damping Mechanism

Springer Science and Business Media LLC - Tập 21 - Trang 1-23 - 2019
Qionglei Chen1, Xiaonan Hao2
1Institute of Applied Physics and Computational Mathematics, Beijing, China
2The Graduate School of China Academy of Engineering Physics, Beijing, China

Tóm tắt

We prove the global well-posedness in the critical Besov spaces for the incompressible Oldroyd-B model without damping mechanism on the stress tensor in $${\mathbb {R}}^d$$ for the small initial data. Our proof is based on the observation that the behaviors of Green’s matrix to the system of $$\big (u,(-\Delta )^{-\frac{1}{2}}{\mathbb {P}}\nabla \cdot \tau \big )$$ as well as the effects of $$\tau $$ change from the low frequencies to the high frequencies and the construction of the appropriate energies in different frequencies.

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