Topics in Mathematics Münster

Research Interests

$\bullet$ Nonlinear partial differential equations.
$\bullet$ Mathematical fluid dynamics.
$\bullet$ Quantitative analysis of transport equations.
$\bullet$ Degenerate parabolic equations.

Selected Publications of Prof. Dr. Christian Seis

$\bullet$ C. Seis. A quantitative theory for the continuity equation. Ann. Inst. H. Poincaré Anal. Non Linéaire, 34(7):1837–1850, 2017.

$\bullet$ A. Schlichting and C. Seis. Convergence rates for upwind schemes with rough coefficients. SIAM J. Numer. Anal., 55(2):812–840, 2017.

$\bullet$ R. L. Jerrard and C. Seis. On the vortex filament conjecture for Euler flows. Arch. Ration. Mech. Anal., 224(1):135–172, 2017.

$\bullet$ L. Mugnai, C. Seis, and E. Spadaro. Global solutions to the volume-preserving mean-curvature flow. Calc. Var. Partial Differential Equations, 55(1):18, 2016.

$\bullet$ C. Seis. Scaling bounds on dissipation in turbulent flows. J. Fluid Mech., 777:591–603, 2015.

$\bullet$ R. J. McCann and C. Seis. The spectrum of a family of fourth-order nonlinear diffusions near the global attractor. Comm. Partial Differential Equations, 40(2):191–218, 2015.

$\bullet$ C. Seis. Long-time asymptotics for the porous medium equation: the spectrum of the linearized operator. J. Differential Equations, 256(3):1191–1223, 2014.

$\bullet$ C. Seis. Maximal mixing by incompressible fluid flows. Nonlinearity, 26(12):3279–3289, 2013.

$\bullet$ F. Otto and C. Seis. Rayleigh- Bénard convection: improved bounds on the Nusselt number. J. Math. Phys., 52(8):083702, 24, 2011.

$\bullet$ Y. Brenier, F. Otto, and C. Seis. Upper bounds on coarsening rates in demixing binary viscous liquids. SIAM J. Math. Anal., 43(1):114–134, 2011.

Current Cluster Publications of Prof. Dr. Christian Seis

$\bullet $ Nicola De Nitti, David Meyer, and Christian Seis. Optimal regularity for the 2d Euler equations in the Yudovich class. Journal de Mathématiques Pures et Appliquées, 191:103631, November 2024. doi:10.1016/j.matpur.2024.103631.

$\bullet $ David Meyer and Christian Seis. Steady ring-shaped vortex sheets. arXiv e-prints, September 2024. arXiv:2409.08220.

$\bullet $ Christian Seis and Dominik Winkler. Fine large-time asymptotics for the axisymmetric Navier–Stokes equations. Journal of Evolution Equations, August 2024. doi:10.1007/s00028-024-01001-5.

$\bullet $ Christian Seis, Emil Wiedemann, and Jakub Woźnicki. Strong convergence of vorticities in the 2D viscosity limit on a bounded domain. arXiv e-prints, June 2024. arXiv:2406.05860.

$\bullet $ David Meyer and Christian Seis. Propagation of regularity for transport equations: a littlewood-paley approach. Indiana Univ. Math. J., 73(2):445–473, May 2024. doi:10.1512/iumj.2024.73.9825.

$\bullet $ Beomjun Choi and Christian Seis. Finite-dimensional leading order dynamics for the fast diffusion equation near extinction. Discrete and Continuous Dynamical Systems, 44(9):2697–2712, April 2024. doi:10.3934/dcds.2024043.

$\bullet $ Christian Seis and Dominik Winkler. Invariant manifolds for the thin film equation. Archive for Rational Mechanics and Analysis, March 2024. doi:10.1007/s00205-024-01968-y.

$\bullet $ Christian Seis and Dominik Winkler. Stability of traveling waves for doubly nonlinear equations. arXiv e-prints, January 2024. arXiv:2401.10597.

$\bullet $ Christian Seis and Dominik Winkler. Fine large-time asymptotics for the axisymmetric Navier–Stokes equations. arXiv e-prints, November 2023. arXiv:2311.03914.

$\bullet $ Lisa Beck, Eleonora Cinti, and Christian Seis. Optimal regularity of isoperimetric sets with Hölder densities. Calculus of Variations and Partial Differential Equations, 62(8):214, August 2023. doi:10.1007/s00526-023-02542-2.

$\bullet $ Christian Seis. Bounds on the rate of enhanced dissipation. Comm. Math. Phys., 399(3):2071–2081, May 2023. doi:10.1007/s00220-022-04588-3.

$\bullet $ Beomjun Choi, Robert J. McCann, and Christian Seis. Correction to: Asymptotics near extinction for nonlinear fast diffusion on a bounded domain. Archive for Rational Mechanics and Analysis, 247(2):28, March 2023. doi:10.1007/s00205-023-01866-9.

$\bullet $ Beomjun Choi, Robert J. McCann, and Christian Seis. Asymptotics near extinction for nonlinear fast diffusion on a bounded domain. Archive for Rational Mechanics and Analysis, 247(2):16, February 2023. doi:10.1007/s00205-023-01850-3.

$\bullet $ Stefano Ceci and Christian Seis. On the dynamics of vortices in viscous 2D flows. Mathematische Annalen, January 2023. doi:10.1007/s00208-023-02568-z.

$\bullet $ Víctor Navarro-Fernández, André Schlichting, and Christian Seis. Optimal stability estimates and a new uniqueness result for advection-diffusion equations. Pure Appl. Anal., 4(3):571–596, December 2022. doi:10.2140/paa.2022.4.571.

$\bullet $ Stefano Ceci and Christian Seis. On the dynamics of point vortices for the two-dimensional Euler equation with $L^p$ vorticity. Philos. Trans. Royal Soc. A, 380(2226):20210046, May 2022. doi:10.1098/rsta.2021.0046.

$\bullet $ David Meyer and Christian Seis. Propagation of regularity for transport equations. a Littlewood-Paley approach. arXiv e-prints, March 2022. arXiv:2203.10860.

$\bullet $ Camilla Nobili and Christian Seis. Renormalization and energy conservation for axisymmetric fluid flows. Math. Ann., 382(1):1–36, February 2022. doi:10.1007/s00208-020-02050-0.

$\bullet $ Christian Seis and Dominik Winkler. A well-posedness result for a system of cross-diffusion equations. J. Evol. Equ., 21(2):2471–2489, May 2021. doi:10.1007/s00028-021-00690-6.

$\bullet $ André Schlichting and Christian Seis. The Scharfetter–Gummel scheme for aggregation–diffusion equations. IMA J. Numer. Anal., May 2021. doi:10.1093/imanum/drab039.

$\bullet $ Helena J Nussenzveig Lopes, Christian Seis, and Emil Wiedemann. On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity. Nonlinearity, 34(5):3112–3121, May 2021. doi:10.1088/1361-6544/abe51f.

$\bullet $ Stefano Ceci and Christian Seis. Vortex dynamics for 2D Euler flows with unbounded vorticity. Rev. Mat. Iberoam., 37(5):1969–1990, May 2021. doi:10.4171/rmi/1255.

$\bullet $ Christian Seis. A note on the vanishing viscosity limit in the Yudovich class. Can. Math. Bulletin, pages 1–11, April 2020. doi:10.4153/S0008439520000296.

$\bullet $ Christian Seis. On the Littlewood–Paley spectrum for passive scalar transport equations. J. Nonlinear Sci., 30(2):645–656, April 2020. doi:10.1007/s00332-019-09585-w.

$\bullet $ Christian Seis. Diffusion limited mixing rates in passive scalar advection. arXiv e-prints, March 2020. arXiv:2003.08794.