# Miles H. Wheeler¶

I am a Lecturer 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¶

My paper 3 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.The One World PDE Seminar meets Tuesdays 3–5pm UK time. Hope to see you there!

## PhD students¶

I am happy to be contacted by potential PhD students, who may also find these informal notes useful. They are from a 2019 lecture to a group of masters students in mathematics and physics, and provide a quick introduction to local and global bifurcation theory.

## Papers and preprints¶

- 1
T Truong, E Wahlén, and MH Wheeler, Global bifurcation of solitary waves for the Whitham equation, submitted. arxiv (38 pages)

- 2
RM Chen, S Walsh, and MH Wheeler, Global bifurcation of anti-plane shear fronts, submitted. arxiv (21 pages)

- 3(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)- 4
A Constantin, DG Crowdy, VS Krishnamurthy, and MH Wheeler, Stuart-type polar vortices on a rotating sphere, to appear in

*Discrete Contin. Dyn. Syst.*journal (15 pages)- 5
VM Hur and MH Wheeler, Exact free surfaces in constant vorticity flows,

*J. Fluid Mech. (Rapids)*896:R1, 2020. postprint, journal (10 pages)- 6
RM Chen, S Walsh, and MH Wheeler, Global bifurcation for monotone fronts of elliptic equations, submitted. arxiv (60 pages)

- 7
V Kozlov, E Lokharu, and MH Wheeler, Nonexistence of subcritical solitary waves, submitted. arxiv (13 pages)

- 8
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)

- 9
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)- 10
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)- 11
MH Wheeler, On stratified water waves with critical layers and Coriolis forces,

*Discrete Contin. Dyn. Syst.*39(8):4747, 2019. journal, preprint (24 pages)- 12
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)- 13
MH Wheeler, Simplified Models for Equatorial Waves with Vertical Structure,

*Oceanography*31(3):36, 2018. journal (open access) (6 pages)- 14
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)- 15
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)- 16
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. announcement (5 pages)- 17
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)- 18
MH Wheeler, The Froude number for solitary water waves with vorticity,

*J. Fluid Mech.*768:91, 2015. arxiv, journal, (22 pages)- 19
MH Wheeler, Solitary water waves of large amplitude generated by surface pressure,

*Arch. Rational Mech. Anal.*218(2):1131, 2015. preprint, journal, (57 pages)- 20
MH Wheeler, Large-amplitude solitary water waves with vorticity.

*SIAM J. Math. Anal.*45(5):2937, 2013. preprint, journal, (58 pages)- 21
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 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).