Miles H. Wheeler

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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.

Email

mw2319@bath.ac.uk

Office

4W 1.12

Office hours

By appointment

Papers and preprints

1

SV Haziot and MH Wheeler, Large-amplitude steady solitary water waves with constant vorticity 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, submitted. arxiv (79 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, submitted. arxiv (34 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. journal (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, journal (35 pages)

8

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

9

RM Chen, S Walsh, and MH Wheeler, Global bifurcation of anti-plane shear fronts, J. Nonlinear Sci. 31:28, 2021. arxiv, journal (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, journal (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. journal (15 pages)

12

VM Hur and MH Wheeler, Exact free surfaces in constant vorticity flows, J. Fluid Mech. (Rapids) 896:R1, 2020. postprint, journal (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., online May 2021. arxiv, journal (18 pages)

15

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)

16

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)

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. journal, preprint (11 pages)

18

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

20

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

21

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)

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, journal (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. journal (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, journal (26 pages)

25

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

26

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

27

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

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

CV

Last updated September 2021

Some figures (mostly from talks)

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_images/elastic.svg
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_images/pressure.jpg
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