# Miles H. Wheeler¶

I am a Lecturer in Analysis in the Department of Mathematical Sciences at the University of Bath. Before coming to Bath, I was a University Assistant at the Faculty of Mathematics at the University of Vienna, and before that I was a postdoc at the Courant Institute of Mathematical Sciences supported by an NSF fellowship. I am interested in partial differential equations coming from fluid mechanics, especially “large-amplitude” solutions that cannot be captured using perturbative techniques.

- Office
4W 1.12

- Office hours
By appointment

## News¶

This summer, Bath is hosting an LMS Symposium on New Directions in Water Waves, consisting of a summer school July 18–22 and workshop July 25–29. The application for the summer school is here.

## Papers and preprints¶

- 1
SV Haziot and MH Wheeler, Large-amplitude steady solitary water waves with constant vorticity, submitted. arxiv (35 pages)

- 2(1,2)
SV Haziot, VM Hur, WA Strauss, JF Toland, E Wahlén, S Walsh, and MH Wheeler, Traveling water waves — the ebb and flow of two centuries, Quart. Appl. Math. 80:317, 2022. arxiv (85 pages)

- 3
VM Hur and MH Wheeler, Overhanging and touching waves in constant vorticity flows, submitted. arxiv (17 pages)

- 4
Z Hassainia and MH Wheeler, Multipole vortex patch equilibria for active scalar equations, submitted. arxiv (32 pages)

- 5
MA Johnson, T Truong, and MH Wheeler, Solitary waves in a Whitham equation with small surface tension, Stud. Appl. Math. 148(2):773, 2022. arxiv (40 pages)

- 6
RM Chen, S Walsh, and MH Wheeler, Large-amplitude internal fronts in two-fluid systems, C. R. Math. Acad. Sci. Paris 358(9-10):1073, 2020. (11 pages)

- 7
VS Krishnamurthy, MH Wheeler, DG Crowdy, and A Constantin, Liouville chains: new hybrid vortex equilibria of the 2D Euler equation, J. Fluid Mech. 921:A1, 2021. arxiv (35 pages)

- 8
T Truong, E Wahlén, and MH Wheeler, Global bifurcation of solitary waves for the Whitham equation, Math. Ann., 2021. arxiv (45 pages)

- 9
RM Chen, S Walsh, and MH Wheeler, Global bifurcation of anti-plane shear fronts, J. Nonlinear Sci. 31:28, 2021. arxiv (31 pages)

- 10
VS Krishnamurthy, MH Wheeler, DG Crowdy, and A Constantin, A transformation between stationary point vortex equilibria, Proc. R. Soc. A. 476:20200310, 2020. postprint, (21 pages)

- 11
A Constantin, DG Crowdy, VS Krishnamurthy, and MH Wheeler, Stuart-type polar vortices on a rotating sphere, Discrete Contin. Dyn. Syst. 41(1):201, 2021. (15 pages)

- 12
VM Hur and MH Wheeler, Exact free surfaces in constant vorticity flows, J. Fluid Mech. (Rapids) 896:R1, 2020. postprint (10 pages)

- 13
RM Chen, S Walsh, and MH Wheeler, Global bifurcation for monotone fronts of elliptic equations, submitted. arxiv (60 pages)

- 14
V Kozlov, E Lokharu, and MH Wheeler, Nonexistence of subcritical solitary waves, Arch. Rational Mech. Anal. 241:535, 2021. arxiv (18 pages)

- 15
RM Chen, S Walsh, and MH Wheeler, Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics, Nonlinearity 35(4):1927, 2022. arxiv (59 pages)

- 16
Z Hassainia, N Masmoudi, and MH Wheeler, Global bifurcation of rotating vortex patches, Comm. Pure Appl. Math. 73(9):1933, 2020. arxiv (48 pages)

- 17
VS Krishnamurthy, MH Wheeler, DG Crowdy, and A Constantin, Steady point vortex pair in a field of Stuart-type vorticity, J. Fluid Mech. (Rapids) 874:R1, 2019. preprint (11 pages)

- 18
MH Wheeler, On stratified water waves with critical layers and Coriolis forces, Discrete Contin. Dyn. Syst. 39(8):4747, 2019. preprint (24 pages)

- 19
RM Chen, S Walsh, and MH Wheeler, Existence, nonexistence, and asymptotics of deep water solitary waves with localized vorticity, Arch. Rational Mech. Anal., 234(2):595, 2019 arxiv (39 pages)

- 20
MH Wheeler, Simplified Models for Equatorial Waves with Vertical Structure, Oceanography 31(3):36, 2018. (6 pages)

- 21
MH Wheeler, Integral and asymptotic properties of solitary waves in deep water, Comm. Pure Appl. Math. 71: 1941, 2018. preprint, arxiv (16 pages)

- 22
RM Chen, S Walsh, and MH Wheeler, Existence and qualitative theory for stratified solitary water waves, Ann. Inst. H. Poincaré Anal. Non Linéaire 35(2):517, 2017. arxiv (62 pages)

- 23
RM Chen, S Walsh, and MH Wheeler, On the existence and qualitative theory for stratified solitary water waves, C. R. Math. Acad. Sci. Paris 354(6):601, 2016. (5 pages)

- 24
WA Strauss and MH Wheeler, Bound on the slope of steady water waves with favorable vorticity, Arch. Rational Mech. Anal. 222:1555, 2016. preprint, arxiv (26 pages)

- 25
MH Wheeler, The Froude number for solitary water waves with vorticity, J. Fluid Mech. 768:91, 2015. arxiv (22 pages)

- 26
MH Wheeler, Solitary water waves of large amplitude generated by surface pressure, Arch. Rational Mech. Anal. 218(2):1131, 2015. preprint (57 pages)

- 27
MH Wheeler, Large-amplitude solitary water waves with vorticity. SIAM J. Math. Anal. 45(5):2937, 2013. preprint (58 pages)

- 28
S Constantin, RS Strichartz, and M Wheeler, Analysis of the Laplacian and spectral operators on the Vicsek set Commun. Pure Appl. Anal. 10(1):1, 2011. arxiv, website (44 pages)

## Expository notes and talks¶

For a more accessible introduction to the sort of work I do, see this expository talk on solitary waves and fronts (and Section 5 of 2), or this short introduction to local and global bifurcation theory. The talk is from a series on steady water waves in the ONEPAS seminar, and the notes are from a 2019 lecture to a group of masters students in mathematics and physics.

## Teaching¶

Spring 2022, University of Bath: Theory of Partial Differential Equations

Fall 2021, University of Bath: Advanced Real Analysis

Spring 2021, University of Bath: Theory of Partial Differential Equations

Fall 2020, University of Bath: Advanced Real Analysis

Spring 2020, University of Bath: Theory of Partial Differential Equations

Summer 2019, University of Vienna: Tutorial on ordinary differential equations.

Winter 2018, University of Vienna: Topics in analysis: fluid mechanics

Summer 2018, University of Vienna: Tutorial on ordinary differential equations.

Winter 2017, University of Vienna: Tutorial on partial differential equations.

Fall 2016, NYU: Instructor for Math-UA 325, Analysis I (Section 3).

Spring 2015, NYU: Instructor for Math-UA 121, Calculus I (Section 6).

Fall 2014, NYU: Instructor for Math-UA 122, Calculus II (Section 3).

Fall 2012, Brown University: Instructor (TF) for Math 200, Intermediate (Multivariable, Physics/Engineering) Calculus.

Spring 2012, Brown University: Instructor (TF) for Math 200, Intermediate (Multivariable, Physics/Engineering) Calculus.

Spring 2012, Brown University: TA for Math 100 (Calculus II).

Fall 2010, Brown University: TA for Math 100 (Calculus II).

David Lowry-Duda and I also wrote an expository paper aimed at
undergraduates which has appeared in the *American Mathematical Monthly*.