Teaching: Course webpages are available at learning.drexel.edu

Refereed Journal Publications

Traveling and time-periodic waves for dispersive PDE and interfacial fluid dynamics

• D.M. Ambrose and J.D. Wright. Nonexistence of small, smooth, time-periodic, spatially periodic solutions for nonlinear Schrodinger equations. Accepted, Quart. Appl. Math., 2018. [Preprint.]
• B.F. Akers, D.M. Ambrose, and D.W. Sulon. Periodic traveling interfacial hydroelastic waves with or without mass II: Multiple bifurcations and ripples. European J. Appl. Math., 30:756-790, 2019. [Arxiv.]
• B.F. Akers, D.M. Ambrose, and D.W. Sulon. Periodic traveling interfacial hydroelastic waves with or without mass. Zeitschrift für angewandte Mathematik und Physik (ZAMP). 68: 141, 2017. [Arxiv.]
• D.M. Ambrose, W.A. Strauss, and J.D. Wright. Global bifurcation theory for periodic traveling interfacial gravity-capillary waves. Ann. Inst. H. Poincare Anal. Non Lineaire, 33:1081-1101, 2016. [Arxiv.]
• B.F. Akers, D.M. Ambrose, K. Pond, and J.D. Wright. Overturned internal capillary-gravity waves. Eur. J. Mech. B Fluids, 57:143-151, 2016. [Preprint.]
• D.M. Ambrose and J.D. Wright. Nonexistence of small doubly periodic solutions for dispersive equations. Analysis & PDE, 9:15-42, 2016. [Arxiv.]
• D.M. Ambrose, M. Kondrla, and M. Valle. Computing time-periodic solutions of a model for the vortex sheet with surface tension. Quart. Appl. Math., 73:317-329, 2015. [Preprint.]
• D.M. Ambrose and J.D. Wright. Non-existence of small-amplitude doubly periodic waves for dispersive equations. C. R. Math. Acad. Sci. Paris, 352:597-602, 2014. [Preprint.]
• B.F. Akers, D.M. Ambrose, and J.D. Wright. Gravity perturbed Crapper waves. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 470: 20130526, 2014. [Preprint.]
• B. Akers, D.M. Ambrose, and J.D. Wright. Traveling waves from the arclength parameterization: Vortex sheets with surface tension. Interfaces Free Bound., 15:359-380, 2013. [Preprint.]
• D.M. Ambrose and J. Wilkening. Computation of time-periodic solutions of the Benjamin-Ono equation. J. Nonlinear Sci., 20:277-308, 2010. [Open access.]
• D.M. Ambrose and J. Wilkening. Computation of symmetric, time-periodic solutions of the vortex sheet with surface tension. Proc. Natl. Acad. Sci. USA, 107:3361-3366, 2010. [Open access.]
• D.M. Ambrose and J. Wilkening. Global paths of time-periodic solutions of the Benjamin-Ono equation connecting pairs of traveling waves. Commun. Appl. Math. Comput. Sci., 4:177-215, 2009. [Arxiv.]

Analysis for the 2D Euler equations and related models

• D.M. Ambrose, M.C. Lopes Filho, and H.J. Nussenzveig Lopes. Confinement of vorticity for the 2D Euler-alpha equations. J. Differential Equations, 265:5472-5489, 2018. [Arxiv.]
• D.M. Ambrose, J.P. Kelliher, M.C.Lopes Filho, and H.J. Nussenzveig Lopes. Serfati solutions to the 2D Euler equations on exterior domains. J. Differential Equations, 259:4509-4560, 2015. [Arxiv.]

Equations with nonlinear/degenerate dispersion

• T. Akhunov, D.M. Ambrose, and J.D. Wright. Well-posedness of fully nonlinear KdV-type evolution equations. Accepted, Nonlinearity, 2019. [Arxiv.]
• D.M. Ambrose, G.R. Simpson, J.D. Wright, and D.G. Yang. Existence theory for magma equations in dimension two and higher. Nonlinearity, 31:4724-4745, 2018. [Arxiv.]
• D.M. Ambrose and J.D. Wright. Dispersion vs. anti-diffusion: Well-posedness in variable coefficient and quasilinear equations of KdV-type. Indiana U. Math. J., 62:1237-1281, 2013. [Arxiv.]
• D.M. Ambrose and J.D. Wright. Traveling waves and weak solutions for an equation with degenerate dispersion. Proc. Amer. Math. Soc., 141:3825-3838, 2013.
• D.M. Ambrose, G. Simpson, J.D. Wright, and D.G. Yang. Ill-posedness of degenerate dispersive equations. Nonlinearity, 25: 2655-2680, 2012. [Arxiv.]
• D.M. Ambrose and J.D. Wright. Preservation of support and positivity for solutions of degenerate evolution equations. Nonlinearity, 23:607-620, 2010.

Mean field games

• D.M. Ambrose. Existence theory for a time-dependent mean field games model of household wealth. Submitted, 2019. [Preprint.]
• D.M. Ambrose. Existence theory for non-separable mean field games in Sobolev spaces. Submitted, 2018. [Preprint.]
• D.M. Ambrose. Strong solutions for time-dependent mean field games with non-separable Hamiltonians. J. Math. Pures Appl., 113:141-154, 2018. [Arxiv.]
• D.M. Ambrose. Small strong solutions for time-dependent mean field games with local coupling. C. R. Math. Acad. Sci. Paris, 354:589-594, 2016. [Preprint.]

Analysis for other nonlinear partial differential equations

• D.M. Ambrose. The radius of analyticity for solutions to a problem in epitaxial growth on the torus. Submitted, 2018. [Preprint.]
• D.M. Ambrose and A.L. Mazzucato. Global existence and analyticity for the 2D Kuramoto-Sivashinsky equation. J. Dynam. Differential Equations, Accepted, 2018. [Arxiv.]
• D.M. Ambrose and G. Simpson. Local existence theory for derivative nonlinear Schrödinger equations with non-integer power nonlinearities. SIAM J. Math. Anal., 47:2241-2264, 2015. [Arxiv.]

Analysis and computing for waves in electromagnetics

• D.M. Ambrose, E. Das Gupta, S. Moskow, V. Ozornina, and G. Simpson. Detection of thin high contrast dielectrics from boundary measurements. Submitted, 2019. [Preprint.]
• D.M. Ambrose, J. Gopalakrishnan, S. Moskow, and S. Rome. Scattering of electromagnetic waves by thin high contrast dielectrics II: Asymptotics of the electric field and a method for inversion. Comm. Math. Sci., 15:1041-1053, 2017. [Preprint.]
• D.M. Ambrose and D.P. Nicholls. Fokas integral equations for three dimensional layered-media scattering. J. Comp. Phys., 276:1-25, 2014. [Preprint.]
• D.M. Ambrose and S. Moskow. Scattering of electromagnetic waves by thin high contrast dielectrics: Effects of the object boundary. Comm. Math. Sci., 11: 293-314, 2013.

Numerical methods for initial value problems in interfacial fluid dynamics

• D.M. Ambrose, Y. Liu, and M. Siegel. Convergence of a boundary integral method for 3D interfacial Darcy flow with surface tension. Math. Comp., 86:2745-2775, 2017. [Preprint.]
• D.M. Ambrose, M. Siegel, and S. Tlupova. A small-scale decomposition for 3D boundary integral computations with surface tension. J. Comp. Phys., 247:168-191, 2013. [Preprint.]
• D.M. Ambrose and M. Siegel. A non-stiff boundary integral method for 3D porous media flow with surface tension. Math. Comput. Simulation, 82:968-983, 2012.

Existence theory in interfacial fluid dynamics

• S. Liu and D.M. Ambrose. The zero surface tension limit of three-dimensional interfacial Darcy flow. Submitted, 2019. [Preprint.]
• S. Liu and D.M. Ambrose. Sufficiently strong dispersion removes ill-posedness in truncated series models of water waves. Discrete Contin. Dyn. Syst., 39:3123-3147, 2019. [Preprint.]
• D.M. Ambrose, J.L. Bona, and T. Milgrom. Global solutions and ill-posedness for the Kaup system and related Boussinesq systems. Indiana U. Math. J., Accepted, 2017. [Preprint.]
• D.M. Ambrose and M. Siegel. Well-posedness of two-dimensional hydroelastic waves. Proc. Roy. Soc. Edinburgh Sect. A., 147:529-570, 2017. [Preprint.]
• S. Liu and D.M. Ambrose. Well-posedness of two-dimensional hydroelastic waves with mass. J. Differential Equations, 262:4656-4699, 2017. [Preprint.]
• D.M. Ambrose, J.L. Bona, and D.P. Nicholls. On ill-posedness of truncated series models for water waves. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 470:20130849, 2014. [Preprint.]
• D.M. Ambrose. The zero surface tension limit of two-dimensional interfacial Darcy flow. J. Math. Fluid Mech., 16:105-143, 2014. [Preprint.]
• T. Milgrom and D.M. Ambrose. Temporal boundary value problems in interfacial fluid dynamics. Appl. Anal., 92:922-948, 2013.
• D.M. Ambrose, J.L. Bona, and D.P. Nicholls. Well-posedness of a model for water waves with viscosity. Discrete Contin. Dyn. Syst. Ser. B, 17:1113-1137, 2012.
• D.M. Ambrose, M.C. Lopes Filho, H.J. Nussenzveig Lopes, and W.A. Strauss. Transport of interfaces with surface tension by 2D viscous flows. Interfaces Free Bound., 12:23-44, 2010.
• D.M. Ambrose. Singularity formation in a model for the vortex sheet with surface tension. Math. Comput. Simulation, 80:102-111, 2009.
• D.M. Ambrose and N. Masmoudi. The zero surface tension limit of three-dimensional water waves. Indiana U. Math. J., 58:479-522, 2009.
• D.M. Ambrose and N. Masmoudi. Well-posedness of 3D vortex sheets with surface tension. Comm. Math. Sci., 5:391-430, 2007. [Open access.]
• D.M. Ambrose. Well-posedness of two-phase Darcy flow in 3D. Quart. Appl. Math., 65:189-203, 2007.
• D.M. Ambrose and N. Masmoudi. The zero surface tension limit of two-dimensional water waves. Comm. Pure Appl. Math, 58:1287-1315, 2005.
• D.M. Ambrose. Well-posedness of two-phase Hele-Shaw flow without surface tension. European J. Appl. Math., 15:597-607, 2004.
• D.M. Ambrose. Well-posedness of vortex sheets with surface tension. SIAM J. Math. Anal., 35:211-244, 2003.

Book Chapters and Other Expository Articles

• D.M. Ambrose. Vortex sheets, Boussinesq equations, and other problems in the Wiener algebra. SIAM DSWeb, 2019. [Link.] [Download.]
• D.M. Ambrose. Vortex sheet formulations and initial value problems: Analysis and computing. Lectures on the theory of water waves, 140-170, London Math. Soc. Lecture Note Ser., 426, Cambridge Univ. Press, Cambridge, 2016.

Refereed Conference Proceedings

• D.M. Ambrose and J. Wilkening. Dependence of time-periodic vortex sheets with surface tension on mean vortex sheet strength. Procedia IUTAM, 11:15-22, 2014. [Preprint.]
• D.M. Ambrose and J. Wilkening. Computation of time-periodic solutions of nonlinear systems of partial differential equations. Proceedings of Hyperbolic Problems: Theory, Numerics, and Applications. Beijing, China (2010). 2012, 273-280, Higher Education Press.
• D.M. Ambrose. Short-time well-posedness of irrotational free-surface problems in 3D fluids. Proceedings of Hyperbolic Problems: Theory, Numerics, and Applications. Lyon, France (2006). 2008, 307-314, Springer-Verlag.
• D.M. Ambrose. Regularization of the Kelvin-Helmholtz instability by surface tension. Phil. Trans. R. Soc. A. 365:2253-2266, 2007. Proceedings of the Semester on Wave Motion, Institute Mittag-Leffler (2005).
• D.M. Ambrose. Short-time well-posedness of free-surface problems in 2D fluids. Proceedings of Hyperbolic Problems: Theory, Numerics, and Applications. Osaka, Japan (2004). 2006, 247-254, Yokohama Publishers.

External Funding

• PI for NSF Grant DMS-1907684, Partial Differential Equation Methods for Mean Field Games. $316,981. August 1, 2019 -- July 31, 2022.
• PI for NSF Grant DMS-1515849, Dynamics of Dispersive PDE. $269,987. August 15, 2015 -- July 31, 2019.
• PI for NSF Grant DMS-1016267, Collaborative Research: Efficient Surface-Based Numerical Methods for 3D Interfacial Flow with Surface Tension. $269,989. October 1, 2010 -- September 30, 2015. [This is a collaborative grant with Michael Siegel of NJIT.]
• PI for NSF Grant DMS-1008387, Dispersive PDE and Interfacial Fluid Dynamics. $159,000. September 15, 2010 -- August 31, 2014.
• PI for NSF grant DMS-0707807, Long-Time Behavior of Free-Surface Problems in Fluid Dynamics. $119,999. June 15, 2007 -- May 31, 2010. [Renumbered as DMS-0926378.]
• PI for NSF grant DMS-0406130, Analytical and Computational Approaches to Free-Surface Problems in Fluid Dynamics. $81,143. June 1, 2004 -- May 31, 2007. [Renumbered as DMS-0610898.]