# 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¶

The One World PDE Seminar meets Tuesdays 3:30–4:30pm UK time. Hope to see you there!

My paper 7 with Vikas Krishnamurthy, Darren Crowdy, and Adrian Constantin is on the cover of the August issue of

*Proceedings of the Royal Society A*! Special thanks to David Lowry-Duda.

## 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, 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.

## Papers and preprints¶

- 1
Z Hassainia and MH Wheeler, Multipole vortex patch equilibria for active scalar equations. arxiv (32 pages)

- 2
MA Johnson, T Truong, and MH Wheeler, Solitary waves in a Whitham equation with small surface tension, submitted. arxiv (34 pages)

- 3
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. journal (11 pages)- 4
VS Krishnamurthy, MH Wheeler, DG Crowdy, and A Constantin, Liouville chains: new hybrid vortex equilibria of the 2D Euler equation, submitted. arxiv (34 pages)

- 5
T Truong, E Wahlén, and MH Wheeler, Global bifurcation of solitary waves for the Whitham equation, submitted. arxiv (38 pages)

- 6
RM Chen, S Walsh, and MH Wheeler, Global bifurcation of anti-plane shear fronts,

*J. Nonlinear Sci.*31:28, 2021. arxiv, journal (31 pages)- 7(1,2)
VS Krishnamurthy, MH Wheeler, DG Crowdy, and A Constantin, A transformation between stationary point vortex equilibria,

*Proc. R. Soc. A.*476:20200310, 2020. postprint, journal (21 pages)- 8
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. journal (15 pages)- 9
VM Hur and MH Wheeler, Exact free surfaces in constant vorticity flows,

*J. Fluid Mech. (Rapids)*896:R1, 2020. postprint, journal (10 pages)- 10
RM Chen, S Walsh, and MH Wheeler, Global bifurcation for monotone fronts of elliptic equations, submitted. arxiv (60 pages)

- 11
V Kozlov, E Lokharu, and MH Wheeler, Nonexistence of subcritical solitary waves, to appear in

*Arch. Rational Mech. Anal.*arxiv (13 pages)- 12
RM Chen, S Walsh, and MH Wheeler, Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics, submitted. arxiv (45 pages)

- 13
Z Hassainia, N Masmoudi, and MH Wheeler, Global bifurcation of rotating vortex patches,

*Comm. Pure Appl. Math.*73(9):1933, 2020. journal, arxiv (48 pages)- 14
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. journal, preprint (11 pages)- 15
MH Wheeler, On stratified water waves with critical layers and Coriolis forces,

*Discrete Contin. Dyn. Syst.*39(8):4747, 2019. journal, preprint (24 pages)- 16
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 journal, arxiv (39 pages)- 17
MH Wheeler, Simplified Models for Equatorial Waves with Vertical Structure,

*Oceanography*31(3):36, 2018. journal (open access) (6 pages)- 18
MH Wheeler, Integral and asymptotic properties of solitary waves in deep water,

*Comm. Pure Appl. Math.*71: 1941–1956, 2018. preprint, arxiv, journal (16 pages)- 19
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, journal (62 pages)- 20
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. journal (5 pages)- 21
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, journal (26 pages)- 22
MH Wheeler, The Froude number for solitary water waves with vorticity,

*J. Fluid Mech.*768:91, 2015. arxiv, journal, (22 pages)- 23
MH Wheeler, Solitary water waves of large amplitude generated by surface pressure,

*Arch. Rational Mech. Anal.*218(2):1131, 2015. preprint, journal, (57 pages)- 24
MH Wheeler, Large-amplitude solitary water waves with vorticity.

*SIAM J. Math. Anal.*45(5):2937, 2013. preprint, journal, (58 pages)- 25
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, journal, website (44 pages)

## Teaching¶

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 an
undergraduates which has appeared in the *American Mathematical Monthly*.