David Ambrose
Associate Professor

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

Refereed Journal Publications

[Chronologically] [By subject]
Submitted papers:
  1. D.M. Ambrose. Strong solutions for time-dependent mean field games with non-separable Hamiltonians. Submitted, 2016. [Arxiv.]
  2. 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. Submitted, 2015. [Preprint.]
Accepted papers:
  1. D.M. Ambrose, Y. Liu, and M. Siegel. Convergence of a boundary integral method for 3D interfacial Darcy flow with surface tension. Math. Comp. Accepted, 2016. [Preprint.]
  2. D.M. Ambrose and M. Siegel. Well-posedness of two-dimensional hydroelastic waves. Proc. Roy. Soc. Edinburgh Sect. A. Accepted, 2015. [Preprint.]
Published papers:
  1. 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.]
  2. 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.]
  3. 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.]
  4. D.M. Ambrose and J.D. Wright. Nonexistence of small doubly periodic solutions for dispersive equations. Analysis & PDE, 9:15-42, 2016. [Arxiv.]
  5. 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.]
  6. 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.]
  7. 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.]
  8. D.M. Ambrose and D.P. Nicholls. Fokas integral equations for three dimensional layered-media scattering. J. Comp. Phys., 276:1-25, 2014. [Preprint.]
  9. 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.]
  10. 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.]
  11. D.M. Ambrose. The zero surface tension limit of two-dimensional interfacial Darcy flow. J. Math. Fluid Mech., 16:105-143, 2014. [Preprint.]
  12. 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.]
  13. 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.]
  14. 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.]
  15. 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.
  16. 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.]
  17. T. Milgrom and D.M. Ambrose. Temporal boundary value problems in interfacial fluid dynamics. Appl. Anal., 92:922-948, 2013.
  18. 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.
  19. D.M. Ambrose, G. Simpson, J.D. Wright, and D.G. Yang. Ill-posedness of degenerate dispersive equations. Nonlinearity, 25: 2655-2680, 2012. [Arxiv.]
  20. 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.
  21. 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.
  22. 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.]
  23. 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.]
  24. 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.
  25. D.M. Ambrose and J.D. Wright. Preservation of support and positivity for solutions of degenerate evolution equations. Nonlinearity, 23:607-620, 2010.
  26. 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.]
  27. D.M. Ambrose. Singularity formation in a model for the vortex sheet with surface tension. Math. Comput. Simulation, 80:102-111, 2009.
  28. D.M. Ambrose and N. Masmoudi. The zero surface tension limit of three-dimensional water waves. Indiana U. Math. J., 58:479-522, 2009.
  29. D.M. Ambrose and N. Masmoudi. Well-posedness of 3D vortex sheets with surface tension. Comm. Math. Sci., 5:391-430, 2007. [Open access.]
  30. D.M. Ambrose. Well-posedness of two-phase Darcy flow in 3D. Quart. Appl. Math., 65:189-203, 2007.
  31. D.M. Ambrose and N. Masmoudi. The zero surface tension limit of two-dimensional water waves. Comm. Pure Appl. Math, 58:1287-1315, 2005.
  32. D.M. Ambrose. Well-posedness of two-phase Hele-Shaw flow without surface tension. European J. Appl. Math., 15:597-607, 2004.
  33. D.M. Ambrose. Well-posedness of vortex sheets with surface tension. SIAM J. Math. Anal., 35:211-244, 2003.

Book Chapters

Accepted papers:
  1. D.M. Ambrose. Vortex sheet formulations and initial value problems: Analysis and computing. To appear, 2015.

Refereed Conference Proceedings

Published papers:
  1. 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.]
  2. 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.
  3. 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.
  4. 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).
  5. 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

Department of Mathematics
Drexel University