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.

Email: mw2319@bath.ac.uk
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).