In this talk we consider inverse problems for the partial differential equations describing the behavior of certain fluids. Our focus will be on the fluid-structure interaction problem and the objective is to determine the moving domain where the equations are satisfied, based on external measurements. We concentrate on a one-dimensional fluid-solid interaction problem for the Burgers equation, and we will prove uniqueness and conditional stability results. This work is in collaboration with J. Apraiz, E. Fernandez-Cara and M. Yamamoto [1]. [1] J. Apraiz, A. Doubova, E. Fernandez-Cara, M. Yamamoto, "Inverse problems for one-dimensional fluid-solid interaction models", Communications on Applied Mathematics and Computation, https://doi.org/10.1007/s42967-024-00437-3