An L2-type low-frequency condition on initial data is almost necessary and sufficient for optimal upper and lower bounds on temporal decay of solutions to the incompressible Oldroyd-B model without viscosity or damping in critical Besov spaces.
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Sharp decay characterization for the incompressible Oldroyd-B model in critical $L^p$ spaces
An L2-type low-frequency condition on initial data is almost necessary and sufficient for optimal upper and lower bounds on temporal decay of solutions to the incompressible Oldroyd-B model without viscosity or damping in critical Besov spaces.