Research Interests

Research Interests

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

Selected Publications

Selected Publications of 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 Publications

Current Publications

$\bullet$ 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 and Applied Analysis, 4(3):571–596, December 2022. doi:10.2140/paa.2022.4.571.

$\bullet$ Christian Seis and Dominik Winkler. Invariant manifolds for the thin film equation. arXiv e-prints, December 2022. arXiv:2212.02262.

$\bullet$ 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.

$\bullet$ Beomjun Choi, Robert J. McCann, and Christian Seis. Asymptotics near extinction for nonlinear fast diffusion on a bounded domain. arXiv e-prints, February 2022. arXiv:2202.02769.

$\bullet$ 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.

$\bullet$ Stefano Ceci and Christian Seis. On the dynamics of point vortices for the 2D Euler equation with $L^p$ vorticity. arXiv e-prints, July 2021. arXiv:2107.12820.

$\bullet$ 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.

$\bullet$ 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.

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

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

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

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

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