Research area C: Models and Approximations
Unit C1: Evolution and asymptotics
Unit C2: Multi-scale phenomena and macroscopic structures
• Transport Equations, mixing and fluid dynamics online
$\bullet$ Nonlinear partial differential equations.
$\bullet$ Mathematical fluid dynamics.
$\bullet$ Quantitative analysis of transport equations.
$\bullet$ Degenerate parabolic equations.
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.
$\bullet $ V. Navarro-Fernández, A. Schlichting, and C. Seis. Optimal stability estimates and a new uniqueness result for advection-diffusion equations. arXiv e-prints, February 2021. URL: http://arxiv.org/abs/2102.07759.
$\bullet $ C. Seis and D. Winkler. A well-posedness result for a system of cross-diffusion equations. arXiv e-prints, November 2020. arXiv:2011.09186v1.
$\bullet $ C. Seis and E. Wiedemann. On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity. arXiv e-prints, July 2020. arXiv:2007.01091.
$\bullet $ C. 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 $ A. Schlichting and C. Seis. The Scharfetter–Gummel scheme for aggregation-diffusion equations. arXiv e-prints, April 2020. arXiv:2004.13981.
$\bullet $ C. 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 $ C. Seis. Diffusion limited mixing rates in passive scalar advection. arXiv e-prints, March 2020. arXiv:2003.08794.
$\bullet $ C. Seis. A note on the vanishing viscosity limit in the Yudovich class. arXiv e-prints, December 2019. arXiv:1912.07345.
$\bullet $ S. Ceci and C. Seis. Vortex dynamics for 2D Euler flows with unbounded vorticity. arXiv e-prints, July 2019. arXiv:1907.10923.
$\bullet $ C. Nobili and C. Seis. Renormalization and energy conservation for axisymmetric fluid flows. arXiv e-prints, June 2019. arXiv:1906.07400.