## Dr Timothy Candy

**Office:**Science III, room 216

**Phone:**479-7781

**Email:**tcandy@maths.otago.ac.nz

### Research Interests

My research lies in the general areas of partial differential equations and harmonic analysis. I am particularly interested in understanding the global dynamics of solutions to nonlinear dispersive partial differential equations (typically nonlinear models arising in mathematical physics such as the Dirac equation, Wave maps equations, Maxwell-Klein-Gordon equation, ...). A key goal is to prove that for large times solutions to nonlinear problems can decouple into a linear or dispersive term, and terms exhibiting nonlinear effects such as focusing/blow-up or soliton like behaviour.

I am also interested in restriction estimates, and in particular, on bilinear and multilinear restriction estimates. These estimates are closely related to estimates for linear dispersive equations (known as Strichartz estimates), and are a key tool in the study of nonlinear dispersive equations.

### Publications

Preprints for all of my publications can be found on the arXiv.

#### Preprints

- T. Candy,
*A note on bilinear wave-Schrödinger interactions*, arXiv:2005.10944 - T. Candy, S. Herr, and K. Nakanishi,
*Global wellposedness for the energy critical Zakharov system below the ground state*, arXiv:2005.09932 - T. Candy, S. Herr, and K. Nakanishi,
*The Zakharov system in dimension d >=4*, arXiv:1912.05820.

#### Published

- T. Candy,
*Multi-scale bilinear restriction estimates for general phases*, Math. Ann.**375**(2019), 777--843. - T. Candy, C. Kauffman, and H. Lindblad,
*Asymptotic behaviour of the Maxwell-Klein-Gordon system*, Commun. Math. Phys.**367**(2019), no. 2, 683--716. - T. Candy and S. Herr,
*On the Division Problem for the Wave Maps Equation*, Annals of PDE**4**(2018), no. 2, 17. - T. Candy and S. Herr,
*On the Majorana condition for nonlinear Dirac systems*, Ann. Inst. H. Poincaré C Anal. non linéaire**35**(2018), no. 6, 1707--1717. - T. Candy and H. Lindblad,
*Long range scattering for the cubic Dirac equation on R^{1+1}*, Differential and Integral Equations**31**(2018), 507--518. - T. Candy and S. Herr,
*Conditional large initial data scattering results for the Dirac-Klein-Gordon system*, Forum of Mathematics, Sigma**6**(2018), e9. - T. Candy and S. Herr,
*Transference of bilinear restriction estimates to quadratic variation norms and the Dirac-Klein-Gordon system*, Anal. PDE**11**(2018), no. 5, 1171--1240. - H-Q. Bui and T. Candy,
*A characteristation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels*, Functional Analysis, Harmonic Analysis, and Image Processing: A Collection of Papers in Honor of Bjorn Jawerth, Contemp. Math., Vol 693, Amer. Math. Soc., Providence, RI, (2017), 109--141. - N. Bournaveas and T. Candy.
*Global well-posedness for the massless cubic Dirac equation*, Int. Math. Res. Notices.**2016**(2016), no. 22, 6735--6828. - N. Bournaveas, T. Candy, and S. Machihara.
*A note on the Chern-Simons-Dirac equations in the Coulomb gauge*, Discrete Contin. Dyn. Syst.-A.**34**(2014), no. 7, 2693-2701. - T. Candy. Bilinear Estimates and applications to global well-posedness for the Dirac-Klein-Gordon equation, J. Hyper. Differential Equations
**10**(2013), no. 1, 1-35. - N. Bournaveas and T. Candy.
*Local well-posedness for the spacetime Monopole equation in Lorenz gauge*, Nonlinear Diff. Equations and Applications**19**(2012), no. 1, 67-78. - N. Bournaveas, T. Candy, and S. Machihara.
*Local and global well-posedness for the Chern-Simons-Dirac system in one dimension*, Diff. Integral Equations**25**(2012), no. 7-8, 699-718. - T. Candy.
*Global existence for an L2 critical nonlinear Dirac equation in one dimension*, Adv. Diff. Equations**16**(2011), no. 7-8, 643-666.