After studying from 1973 to 1977 at secondary school in Nové Strašecí, Feireisl studied mathematics at Charles University in Prague from 1977 and graduated there in 1982. He received his doctorate in 1986 from the Institute of Mathematics of the Czechoslovak Academy of Sciences with thesis Critical points of non-differentiable functionals: existence of solutions to problems of mathematical elasticity theory under the supervision of Vladimir Lovicar. During the 1980s he worked as an assistant professor at the Department of Mathematics of the Faculty of Mechanical Engineering Czech Technical University in Prague (CTU). He studied at the Institute of Mathematics of the Czechoslovak Academy of Sciences (as a member since 1988) and habilitated there in 1999. He became a lecturer at the Charles University in 2009 and was appointed there to a full professorship in 2011.
