We are interested in minimizing fluid turbulence in the case of an elastic body moving and deforming inside an inviscid fluid, using a distributed control. This translates into analyzing an optimal control problem subject to a moving boundary fluid-structure interaction (FSI). These interactions are highly nonlinear couplings of parabolic-hyperbolic type, described by a mismatch of regularity of the two solutions at the common interface.▒ The control is inherently a nonlinear control, acting as feedback on the moving frame. Its action depends on the flow map of the domain, which is itself defined through the dynamics of the problem. We discuss our strategies and results related to the well-posedness of the FSI, the existence of optimal control, and the derivation of the necessary optimality conditions.
BIO: Lorena Bociu received her Ph.D. from the University of Virginia in 2008, and subsequently held postdoctoral positions at University of Nebraska-Lincoln and the CNRS- Institut Non Linéaire de Nice (INLN) as a NSF International Research Fellow. She is an associate professor of mathematics at NC State University and was named a NCSU Diversity Mentoring Fellow and a NCSU Faculty Scholar. She received a National Science Foundation Faculty Early Career Development (CAREER) Award in 2016 and a Presidential Early Career Award for Scientists and Engineers (PECASE) in 2019. Her research interests include analysis and control of nonlinear PDEs: wellposedness, regularity, and sensitivity analysis and control in free boundary problems, with focus on fluid-elasticity interactions, especially in biomechanics.