Andrew Lawrie
I am an Associate Professor of Mathematics at MIT. I did my PhD in Mathematics at the University of Chicago. My advisor was
Wilhelm Schlag.
My research is supported in part by the NSF and the Sloan Foundation.
Contact Information
Department of Mathematics
Massachusetts Institute of Technology
2267
Cambridge, MA 02139
Email: alawrie at mit dot edu
Vita:
Papers and Preprints
The following are all available on my
arXiv.org page.

Continuous in time bubble decomposition for the harmonic map heat flow.
(with J. Jendrej and W. Schlag);
preprint 2023.

Dynamics of kink clusters for scalar fields in dimension 1+1.
(with J. Jendrej);
preprint 2023.

Bubble decomposition for the harmonic map heat flow in the equivariant case.
(with J. Jendrej);
Calc. Var. PDE, to appear.

Soliton resolution for the energycritical nonlinear wave equation in the radial case.
(with J. Jendrej);
Annals of PDE, to appear.

Soliton resolution for energycritical wave maps in the equivariant case.
(with J. Jendrej);
J. Amer. Math. Soc. (JAMS), to appear.

Continuous time soliton resolution for twobubble equivariant wave maps.
(with J. Jendrej);
Math. Res. Lett., to appear.

Uniqueness of twobubble wave maps in high equivariance classes.
(with J. Jendrej);
Comm. Pure Appl. Math. (CPAM), to appear.

An asymptotic expansion of twobubble wave maps in high equivariance classes.
(with J. Jendrej);
Analysis & PDE, to appear.

Dynamics of strongly interacting kinkantikink pairs for scalar fields on a line.
(with J. Jendrej and M. Kowalczyk);
Duke Math. J., to appear.

Asymptotic stability of harmonic maps on the hyperbolic plane under the Schrödinger maps evolution.
(with J. Luhrmann, S.J. Oh and S. Shahshahani);
Comm. Pure Appl. Math. (CPAM), to appear.

Dynamics of bubbling wave maps with prescribed radiation.
(with with J. Jendrej and C. Rodriguez);
Ann. Sci. Éc. Norm. Supér., to appear.

Scattering for defocusing energy subcritical nonlinear wave equations.
(with with B. Dodson, D. Mendelson, and J. Murphy);
Analysis & PDE, 13 (2020), no. 7, 19952090

Local smoothing estimates for Schrodinger equations on hyperbolic space.
(with J. Luhrmann, S.J. Oh and S. Shahshahani);
Mem. Amer. Math. Soc., to appear.

Two bubble dynamics for threshold solutions to the wave maps equation
(with J. Jendrej);
Invent. Math. 213 (2018) no. 3, 12491325 link to online version

Conditional stable soliton resolution for a semilinear Skyrme equation
(with C. Rodriguez);
Annals of PDE, 5 (2019), no. 2, Paper No. 15, 59 pp.

The Cauchy problem for wave maps on hyperbolic space in dimensions d ≥ 4.
(with S.J. Oh and S. Shahshahani);
IMRN Vol. 2018, No. 7, 19542051

Equivariant wave maps on the hyperbolic plane with large energy
(with S.J. Oh and S. Shahshahani);
Math. Res. Lett. 24 (2017) no. 2, 449479

A refined threshold theorem for (1+2)dimensional wave maps into surfaces
(with S.J. Oh);
Comm. Math. Phys. 342 (2016) no. 3, 989999.

Gap eigenvalues and asymptotic dynamics of geometric wave equations on hyperbolic space
(with S.J. Oh and S. Shahshahani);
J. Funct. Anal. 271 (2016), no. 11, 31113161.

Profile decompositions for wave equations on hyperbolic space with applications
(with S.J. Oh and S. Shahshahani);
Math. Ann. 365 (2016), no. 12, 707803.

Stable soliton resolution for exterior wave maps in all equivariance classes.
(with C. Kenig, B. Liu, and W. Schlag);
Advances in Math. 285 (2015), 235300.

Channels of energy for the linear radial wave equation.
(with C. Kenig, B. Liu, and W. Schlag);
Advances in Math. 285 (2015), 877936.

Scattering for radial, semilinear, supercritical wave equations with bounded critical norm.
(with B. Dodson);
Arch. Rational Mech. and Anal. 218 (2015) no. 3, 14591529.

Scattering for the radial 3d cubic wave equation.
(with B. Dodson);
Analysis & PDE. 8 (2015) no. 2, 467497.

Stability of stationary equivariant wave maps from the hyperbolic plane.
(with S.J. Oh and S. Shahshahani);
Amer. J. Math. 139 (2017) no. 4, 10851147.

Profiles for the radial focusing 4d energycritical wave equation.
(with R. Cote, C. Kenig, and W. Schlag);
Comm. Math. Phys. 357 (2018), no. 3, 9431008.

Conditional global existence and scattering for a semilinear Skyrme equation with large data.
Comm. Math. Phys.. 334 (2015) no. 2, 10251081.

Relaxation of wave maps exterior to a ball to harmonic maps for all data.
(with C. Kenig and W. Schlag);
Geom. Funct. Anal. (GAFA). 24 (2014), no. 2, 610647.

Characterization of large energy solutions of the equivariant wave maps problem: I.
(with R. Cote, C. Kenig, and W. Schlag);
Amer. J. Math. 137 (2015) no. 1, 139207.

Characterization of large energy solutions of the equivariant wave maps problem: II.
(with R. Cote, C. Kenig, and W. Schlag);
Amer. J. Math. 137 (2015) no. 1, 209250.

Scattering for wave maps exterior to a ball.
(with W. Schlag);
Advances in Math. 232 (2013), no. 1, 5797.

The Cauchy problem for wave maps on a curved background.
Calc. Var. Partial Differential Equations. 45 (2012), no. 34, 505548.
Seminars
Thesis and Expository Notes

On the Global Behavior of Wave Maps.
My PhD thesis from the University of Chicago.

Nonlinear Wave Equations.
These notes give a brief introduction to nonlinear wave equations. They were written during my second year at the University of Chicago as part of my topics examination and comprise part of my own introduction to the subject. They cover the local wellposedness theory for semilinear wave equations with smooth data as well as Strichartz estimates with applications including small data global existence and scattering for wave equations with power type nonlinearities.