This paper deals with the controllability of the second-grade fluids, a class of non-Newtonian of differential type, on a two-dimensional torus. Using the method of Agrachev and Sarychev (J. Math Fluid Mech., 7(1):108–52 (2005)), Agrachev and Sarychev (Commun Math Phys., 265(3):673–97 (2006)), and of Shirikyan (Commun Math Phys., 266(1):123–51 (2006)), we prove that the system of second-grade fluids is approximately controllable by a finite-dimensional control force.
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This work was partially done during the visit of the first author at the Vietnam Institute for Advanced Study in Mathematics (VIASM). The first author is thankful to the VIASM for the support and for the very kind hospitality of the institute and of all the staff.
The first author received financial support from VIASM.
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Ngo, V., Raugel, G. Approximate Controllability of Second-Grade Fluids. J Dyn Control Syst (2020). https://doi.org/10.1007/s10883-020-09503-4
- Second grade fluid equations
- Approximate controllability
- Agrachev-Sarychev method
Mathematics Subject Classification (2010)