1. Global well-posedness of 2D incompressible Oldroyd-B model with only velocity dissipation.
- Author
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Chen, Yuhao and Zhu, Yi
- Subjects
- *
VELOCITY , *CAUCHY problem , *STRAINS & stresses (Mechanics) , *COMMUTATION (Electricity) - Abstract
The small data global well-posedness in Sobolev setting for the incompressible Oldroyd-B equations with only velocity dissipation (namely there is no damping or dissipation of stress tensor) on R 2 remains open by now. The approach for the similar problem on R 3 becomes invalid due to the fewer decay rates. In this paper, we will give a positive answer to this problem. Namely, we shall focus on the Cauchy problem for the incompressible Oldroyd-B equations with only velocity dissipation on R 2 and derive the small data global well-posedness under Sobolev setting. We also give the time decay estimate for the solutions. To achieve this goal, we explore the dissipative structure of system and develop the fractional time-weighted energy framework. Moreover, some delicate commutator and bilinear estimates are proposed to deal with the wildest nonlinear terms. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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