Professor

**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.

- 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.
- L.C. Brown and D.M. Ambrose. Equilibria in the large-scale competition for market share in a commodity with resource-buying. Submitted, 2022.
- D.M. Ambrose, F. Hadadifard, and J.P. Kelliher. Contour dynamics and global regularity for periodic vortex patches and layers. Submitted, 2022. [Arxiv.]
- 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.]

- 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.] - 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. - 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.]

- 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.] - 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.] - 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.] - 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.] - 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.] - D.M. Ambrose. Existence theory for non-separable mean field games in Sobolev spaces.
*Indiana U. Math. J.*,**71**:611-647, 2022. [Arxiv.] - 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.] - D.M. Ambrose, F. Cakoni, and S. Moskow. A perturbation problem for transmission eigenvalues.
*Res. Math. Sci.*,**9**, paper no. 11, 2022. [Preprint.] - 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.] - 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.] - B.F. Akers and D.M. Ambrose. Efficient computation of coordinate-free models of flame fronts.
*ANZIAM J.*,**63**:58-69, 2021. [Preprint.] - D.M. Ambrose. Existence theory for a time-dependent mean field games
model of household wealth.
*Appl. Math. Optim.*,**83**:2051-2081, 2021. [Arxiv.] - 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.] - 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.] - 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.] - T. Akhunov, D.M. Ambrose, and J.D. Wright. Well-posedness of fully nonlinear KdV-type evolution equations.
*Nonlinearity*,**32**:2914-2954, 2019. [Arxiv.] - 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.] - 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.] - 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.] - 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.] - 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, 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, 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. Strong solutions for time-dependent mean field
games with non-separable Hamiltonians.
*J. Math. Pures Appl.*,**113**:141-154, 2018. [Arxiv.] - 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.] - 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, 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 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, 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.] - 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.] - 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, 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.] - 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.] -
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 D.P. Nicholls.
Fokas integral equations for three dimensional layered-media scattering.
*J. Comp. Phys.*,**276**:1-25, 2014. [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.] - 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.] - 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.] - 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.] - 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.D. Wright. Traveling waves and weak solutions for an equation with degenerate dispersion.
*Proc. Amer. Math. Soc.*,**141**:3825-3838, 2013. - 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.] - T. Milgrom and D.M. Ambrose. Temporal boundary value problems in interfacial fluid dynamics.
*Appl. Anal.*,**92**:922-948, 2013. - 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.

- 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 M. Siegel.
A non-stiff boundary integral method for 3D porous media flow with surface tension.
*Math. Comput. Simulation*,**82**:968-983, 2012.

- 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 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, 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 and J.D. Wright. Preservation of support and positivity for solutions of degenerate evolution equations.
*Nonlinearity*,**23**:607-620, 2010.

- 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.] - 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.

- 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.

- 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-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.]

Drexel University