91ÖÆƬ³§

Education:

• PhD, Mathematics, Duke University, 2002
• MA, Mathematics, Duke University, 1999
• MS, Mathematics, Carnegie Mellon University, 1997
• BS, Mathematics and Economics, Carnegie Mellon University, 1997

Curriculum Vitae:

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Research Interests:

• Mathematical analysis
• Fluid dynamics
• Nonlinear partial differential equations
• Boundary integral methods

Bio:

David M. Ambrose works in mathematical analysis and scientific computing for nonlinear systems of partial differential equations arising in various applications, with a focus on moving-boundary problems in fluid dynamics. He has made contributions to the theory of the Euler and Navier-Stokes equations (including in settings with a free boundary), dispersive model equations, the Kuramoto-Sivashinsky equation and other models for the motion of flame fronts, equations with degenerate dispersion, and mean field games. With collaborators he has also designed and analyzed numerical algorithms for the motion of free surfaces in fluid dynamics. His work has resulted in more than 70 refereed journal publications and more than twenty years of continuous support from the National Science Foundation. He received the T. Brooke Benjamin Prize in Nonlinear Waves from the Society for Industrial and Applied Mathematics in 2018.

Dr. Ambrose first joined the Department of Mathematics at 91ÖÆƬ³§ in 2008. He was previously a faculty member at Clemson University and a Courant Instructor at the Courant Institute of New York University. He received his PhD under the supervision of J. Thomas Beale at Duke University in 2002.

Selected Publications:

• D.M. Ambrose, P.M. Lushnikov, M. Siegel, and D.A. Silantyev. (2024) “Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains.” Nonlinearity, 37:025004.
• D.M. Ambrose, E. Cozzi, D. Erickson, and J.P Kelliher. (2023) “Existence of solutions to fluid equations in Holder and uniformly local Sobolev spaces.” Journal of Differential Equations, 364:107-151.
• D.M. Ambrose and A.R. Meszaros. (2023) “Well-posedness of mean field games master equations involving non-separable local Hamiltonians.” Transactions of the American Mathematical Society, 376:2481-2523.
• D.M. Ambrose, R. Camassa, J.L. Marzuola, R. McLaughlin, Q. Robinson, and J. Wilkening. (2022) “Numerical algorithms for water waves with background flow over obstacles and topography.” Advances in Computational Mathematics, 48:46.
• D.M. Ambrose and A.L. Mazzucato. (2021) “Global solutions of the two-dimensional Kuramoto-Sivashinsky equation with a linearly growing mode in each direction.” Journal of Nonlinear Science, 31:96.
• D.M. Ambrose. (2021) “Existence theory for a time-dependent mean field games model of household wealth.” Applied Mathematics & Optimization, 83:2051-2081.
• T. Akhunov, D.M. Ambrose, and J.D. Wright. (2019). “Well-posedness of fully nonlinear KdV-type evolution equations.” Nonlinearity, 32:2914-2954.
• D.M. Ambrose. (2018). “Strong solutions for time-dependent mean field games with non-separable Hamiltonians.” Journal de Mathematiques Pures et Appliquees, 113:141-154.
• D.M. Ambrose, Y. Liu, and M. Siegel. (2017). “Convergence of a boundary integral method for 3D interfacial Darcy flow with surface tension.” Mathematics of Computation, 86:2745-2775.
• D.M. Ambrose, W.A. Strauss, and J.D. Wright. (2016). “Global bifurcation theory for periodic traveling interfacial gravity-capillary waves.” Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 33:1081-1101.
• B.F. Akers, D.M. Ambrose, and J.D. Wright. (2014). “Gravity perturbed Crapper waves.” Proceedings of the Royal Society A, 470:20130526.
• D.M. Ambrose, M. Siegel, and S. Tlupova. (2013). “A small-scale decomposition for 3D boundary integral computations with surface tension.” Journal of Computational Physics, 247:168-191.
• D.M. Ambrose, G. Simpson, J.D. Wright, and D.G. Yang. (2012). “Ill-posedness of degenerate dispersive equations.” Nonlinearity, 25:2655-2680.
• D.M. Ambrose and J. Wilkening. (2010). “Computation of symmetric, time-periodic solutions of the vortex sheet with surface tension.” Proceedings of the National Academy of Sciences of the USA, 107:3361-3366. https://www.pnas.org/doi/full/10.1073/pnas.0910830107
• D.M. Ambrose and N. Masmoudi. (2005). “The zero surface tension limit of two-dimensional water waves.” Communications on Pure and Applied Mathematics, 58:1287-1315.