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

Conferences: The First Drexel Waves Workshop was a success, and we look forward to hosting the Second Drexel Waves Workshop in 2023.

Refereed Journal Publications

Submitted papers:

69. J. Sin, J.W. Bonnes, L.C. Brown, and D.M. Ambrose. Existence and computation of stationary solutions for congestion-type mean field games via bifurcation theory and forward-forward problems. Submitted, 2023.
68. L.C. Brown and D.M. Ambrose. Equilibria in the large-scale competition for market share in a commodity with resource-buying. Submitted, 2022.
67. D.M. Ambrose, F. Hadadifard, and J.P. Kelliher. Contour dynamics and global regularity for periodic vortex patches and layers. Submitted, 2022. [Arxiv.]
66. D.M. Ambrose, P.M. Lushnikov, M. Siegel, and D.A. Silantyev. Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains. Submitted, 2022. [Arxiv.]

Accepted papers:

65. D.M. Ambrose, E. Cozzi, D. Erickson, and J.P. Kelliher. Existence of solutions to fluid equations in Hölder and uniformly local Sobolev spaces. Accepted, J. Differential Equations, 2023. [Arxiv.]
64. S. Liu and D.M. Ambrose. Well-posedness of a model equation for water waves in fluids with odd viscosity. Accepted, J. Dynam. Differential Equations, 2023.
63. D.M. Ambrose, M.C. Lopes Filho, and H.J. Nussenzveig Lopes. Existence and analyticity of the Lei-Lin solution of the Navier-Stokes equations on the torus. Accepted, Proc. Amer. Math. Soc., 2022. [Arxiv.]

Published papers:

62. D.M. Ambrose and A.R. Meszaros. Well-posedness of mean field games master equations involving non-separable local Hamiltonians. Trans. Amer. Math. Soc., 376:2481-2523, 2023. [Arxiv.]
61. S. Liu and D.M. Ambrose. Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts. Phys. D, 447:133682, 2023. [Preprint.]
60. D.M. Ambrose, M. Siegel, and K. Zhang. Convergence of the boundary integral method for interfacial Stokes flow. Math. Comp., 92:695-748, 2023. [Arxiv.]
59. H. Kim and D.M. Ambrose. Well-posedness, ill-posedness, and traveling waves for models of pulsatile flow in viscoelastic vessels. Z. Angew. Math. Phys., 73, paper no. 247, 2022. [Arxiv.]
58. D.M. Ambrose, R. Camassa, J.L. Marzuola, R.M. McLaughlin, Q. Robinson, and J. Wilkening. Numerical algorithms for water waves with background flow over obstacles and topography. Adv. Comput. Math., 48, paper no. 46, 2022. [Open access.]
57. D.M. Ambrose. Existence theory for non-separable mean field games in Sobolev spaces. Indiana U. Math. J., 71:611-647, 2022. [Arxiv.]
56. D.M. Ambrose and J. Woods. Well-posedness and ill-posedness for linear fifth-order dispersive equations in the presence of backwards diffusion. J. Dynam. Differential Equations, 34:897-917, 2022. [Preprint.]
55. D.M. Ambrose, F. Cakoni, and S. Moskow. A perturbation problem for transmission eigenvalues. Res. Math. Sci., 9, paper no. 11, 2022. [Preprint.]
54. D.M. Ambrose, F. Hadadifard, and J.D. Wright. Well-posedness and asymptotics of a coordinate-free model of flame fronts. SIAM J. Appl. Dyn. Syst., 20:2261-2294, 2021. [Arxiv.]
53. D.M. Ambrose and A.L. Mazzucato. Global solutions of the two-dimensional Kuramoto-Sivashinsky equation with a linearly growing mode in each direction. J. Nonlinear Sci., 31, paper no. 96, 2021. [Arxiv.]
52. B.F. Akers and D.M. Ambrose. Efficient computation of coordinate-free models of flame fronts. ANZIAM J., 63:58-69, 2021. [Preprint.]
51. D.M. Ambrose. Existence theory for a time-dependent mean field games model of household wealth. Appl. Math. Optim., 83:2051-2081, 2021. [Arxiv.]
50. S. Liu and D.M. Ambrose. The zero surface tension limit of three-dimensional interfacial Darcy flow. J. Differential Equations, 268:3599-2645, 2020. [Preprint.]
49. D.M. Ambrose, E. Das Gupta, S. Moskow, V. Ozornina, and G. Simpson. Detection of thin high contrast dielectrics from boundary measurements. J. Phys. Comm., 3:115016, 2019. [Open access.]
48. D.M. Ambrose. The radius of analyticity for solutions to a problem in epitaxial growth on the torus. Bull. Lond. Math. Soc., 51:877-886, 2019. [Arxiv.]
47. T. Akhunov, D.M. Ambrose, and J.D. Wright. Well-posedness of fully nonlinear KdV-type evolution equations. Nonlinearity, 32:2914-2954, 2019. [Arxiv.]
46. D.M. Ambrose and J.D. Wright. Nonexistence of small, smooth, time-periodic, spatially periodic solutions for nonlinear Schrodinger equations. Quart. Appl. Math., 77:579-590, 2019. [Preprint.]
45. D.M. Ambrose and A.L. Mazzucato. Global existence and analyticity for the 2D Kuramoto-Sivashinksy equation. J. Dynam. Differential Equations, 31:1525-1547, 2019. [Arxiv.]
44. 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., 68:1173-1198, 2019. [Preprint.]
43. 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.]
42. 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.]
41. 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.]
40. 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.]
39. D.M. Ambrose. Strong solutions for time-dependent mean field games with non-separable Hamiltonians. J. Math. Pures Appl., 113:141-154, 2018. [Arxiv.]
38. B.F. Akers, D.M. Ambrose, and D.W. Sulon. Periodic traveling interfacial hydroelastic waves with or without mass. Z. Angew. Math. Phys., 68: 141, 2017. [Arxiv.]
37. 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.]
36. 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.]
35. D.M. Ambrose and M. Siegel. Well-posedness of two-dimensional hydroelastic waves. Proc. Roy. Soc. Edinburgh Sect. A., 147:529-570, 2017. [Preprint.]
34. S. Liu and D.M. Ambrose. Well-posedness of two-dimensional hydroelastic waves with mass. J. Differential Equations, 262:4656-4699, 2017. [Preprint.]
33. 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.]
32. 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.]
31. 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.]
30. D.M. Ambrose and J.D. Wright. Nonexistence of small doubly periodic solutions for dispersive equations. Analysis & PDE, 9:15-42, 2016. [Arxiv.]
29. 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.]
28. 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.]
27. 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.]
26. D.M. Ambrose and D.P. Nicholls. Fokas integral equations for three dimensional layered-media scattering. J. Comp. Phys., 276:1-25, 2014. [Preprint.]
25. 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.]
24. 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.]
23. D.M. Ambrose. The zero surface tension limit of two-dimensional interfacial Darcy flow. J. Math. Fluid Mech., 16:105-143, 2014. [Preprint.]
22. 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.]
21. 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.]
20. 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.]
19. 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.
18. 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.
16. 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.
    
15. D.M. Ambrose, G. Simpson, J.D. Wright, and D.G. Yang. Ill-posedness of degenerate dispersive equations. Nonlinearity, 25: 2655-2680, 2012. [Arxiv.]
14. 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.
    
13. 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.
    
12. 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.]
11. 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.]
10. 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.
    
9. D.M. Ambrose and J.D. Wright. Preservation of support and positivity for solutions of degenerate evolution equations. Nonlinearity, 23:607-620, 2010.
   
8. 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.]
7. D.M. Ambrose. Singularity formation in a model for the vortex sheet with surface tension. Math. Comput. Simulation, 80:102-111, 2009.
   
6. D.M. Ambrose and N. Masmoudi. The zero surface tension limit of three-dimensional water waves. Indiana U. Math. J., 58:479-522, 2009.
   
5. D.M. Ambrose and N. Masmoudi. Well-posedness of 3D vortex sheets with surface tension. Comm. Math. Sci., 5:391-430, 2007. [Open access.]
   
4. D.M. Ambrose. Well-posedness of two-phase Darcy flow in 3D. Quart. Appl. Math., 65:189-203, 2007.
   
3. D.M. Ambrose and N. Masmoudi. The zero surface tension limit of two-dimensional water waves. Comm. Pure Appl. Math, 58:1287-1315, 2005.
   
2. D.M. Ambrose. Well-posedness of two-phase Hele-Shaw flow without surface tension. European J. Appl. Math., 15:597-607, 2004.
   
1. 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

Published papers:

2. D.M. Ambrose. Vortex sheets, Boussinesq equations, and other problems in the Wiener algebra. SIAM DSWeb, 2019. [Link.] [Download.]
1. 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

Published papers:

5. 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.]
4. 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.
2. 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).
1. 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-2307638, Well-Posedness and Singularity Formation in Applied Free Boundary Problems. $300,000. August 1, 2023 -- July 31, 2026.
• PI for NSF grant DMS-1907684, Partial Differential Equation Methods for Mean Field Games. $316,981. August 1, 2019 -- July 31, 2023.
• 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.]