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