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Memorial seminar dedicated to Prof. Jindřich Nečas - 20th anniversary of his death

Monday, 5. December 2022 - 15:30 to 19:00
Institute of Mathematics, Žitná 25, Praha 1, library
Necas Seminar on Continuum Mechanics together with Mathematical branch of Prague  of  the Union of Czech Mathematicians and Physicists will organize  Memorial seminar dedicated to  Prof. Jindřich Nečas - 20th  anniversary of his death (5.12.2002).

15:30 Opening: Doc. RNDr. Mirko Rokyta, CSc., dean of faculty of Mathematics and Physics
15:40-16:40  Dallas Albritton (Princeton University): Non-uniqueness of Leray solutions to the forced Navier-Stokes equations
Abstract: In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force.
This is joint work with Elia Brué and Maria Colombo.
16:40-17:10  Coffee break
17:10-18:10  Michael Ruzicka (Albert-Ludwigs-University Freiburg): Existence Proofs for Pseudomonotone Parabolic Problems
Abstract:  In the talk we discuss nonlinear parabolic problems which contain a pseudomonotone operator. A new notion of Bochner pseudomonotonicity is introduced and applied. Extensions to quasi non-conforming and non-conforming Bochner pseudomonotonicity yield convergence proofs for fully discrete Rothe–Galerkin schemes in the framework of discretely divergence free FE and DG methods.
[1] E. Baumle and M. Růžička: Note on the existence theory for evolution equations with pseudomonotone operators, Ric. Mat., 2017.
[2] S. Bartels, M. Růžička: Convergence of fully discrete implicit and semi-implicit approximations of singular parabolic equations, SIAM J. Numer. Anal., 2020.
[3] A. Kaltenbach, M. Růžička: Note on the existence theory for pseudo-monotone evolution problems, J. Evol. Equ., 2021.
[4] L.C. Berselli, A. Kaltenbach, M. Růžička: Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications, Math. Models Methods Appl. Sci., 2021.
[5] A. Kaltenbach, M. Růžička: Analysis of fully discrete, non-conforming approximation of evolution equations and applications, in preparation, 2022.

The lectures will be delivered in person/online  in the Institute and streamed via Zoom.

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Meeting ID: 964 0885 7272
Passcode: 876912

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