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 was in 2004/05 at the TU Munich, from 2008 to 2010 a visiting professor at the Central European University in Budapest, and in 2012 at the Erwin Schrödinger Institute in Vienna.
For 2018 to 2021 he was appointed an Einstein Visiting Fellow at TU Berlin.His research deals with partial differential equations, infinite dimensional dynamical systems, and mathematical problems of hydrodynamics.
He received in 2004 and 2009 the Prize of the Academy of Sciences of the Czech Republic, in 2015 the Neuron Award, and in 2017 the gold medal of Charles University, as well as the Bernard Bolzano Honorary Medal from the Czech Academy of Sciences.
In 2012, he chaired the scientific committee of the European Congress of Mathematicians in Krakow.
He was an invited speaker in 2002 at the International Congress of Mathematicians in Beijing.
In 2018 he was a member of the Fields Medal Selection Committee.
In 2013 he received an Advanced Grant from the European Research Council (ERC) for the study of mathematical modeling of gas movement and heat exchange.