My research is primarily in the study of continuum mechanics, mathematical physics and partial differential equations. In particular, I study theoretical and mathematical aspects of continuum mechanics, concentrating on non-classical models including Cosserat rods and gradient continua. The models I’ve worked on go beyond traditional theories of elastic and viscoelastic Cauchy continua, offering the potential to describe complex phenomena—such as fracture or the combined stretching, bending, and twisting of thin rods—in a simple and geometric manner. Moreover, they lead to the creation of new and intriguing partial differential equations.

**Publications**

- A midsurface elasticity model for a thin, nonlinear, gradient elastic plate

**Int. J. Eng. Sci.**, 197 (2024), 104026, 17 pp. - Elastic solids with strain-gradient elastic boundary surfaces

Preprint, 2023, 24 pages. - On evolving natural curvature for an inextensible, unshearable, viscoelastic rod

(with K. R. Rajagopal)

**J. Elast.**, to appear. - Special Cosserat rods with rate-dependent evolving natural configurations

(with K. R. Rajagopal)

**Int. J. Eng. Sci.**, 191 (2023), 103890, 19 pp. - On an elastic strain-limiting special Cosserat rod model

(with K. R. Rajagopal)

**Math. Models Methods Appl. Sci.**, 33 (2023), p. 1-30. - Global well-posedness for two dimensional flows of viscoelastic rate-type fluids

with stress diffusion (with M. Bulícek, J. Málek)

**J. Math. Fluid Mech.**, 24 (2022), Paper No. 61, 19 pp. - Longitudinal shock waves in a class of semi-infinite stretch-limited elastic strings

**Math. Mech. Solids**, 27 (2022), p. 474–490. - Dynamics of bubbling wave maps with prescribed radiation (with J. Jendrej, A. Lawrie)

**Ann. Sci. de l’ENS.**, (4) 55 (2022), p. 1135-1198. - On stretch-limited elastic strings

**Proc. R. Soc. Lond. A**(2021), 477: 20210181, 15 pp. - Local well-posedness in Sobolev spaces for first-order conformal causal relativistic

viscous hydrodynamics (with F. Bemfica, M. Disconzi, Y. Shao)

**Commun. Pure Appl. Anal.**20 (2021), p. 2279-2290. - Threshold dynamics for corotational wave maps

**Analysis and PDE**, 14 (2021), 2123-2161. - Conditional stable soliton resolution for a semi-linear Skyrme equation (with A. Lawrie)

**Ann. PDE**(2019), Paper No. 15, 59 pp. - Soliton resolution for corotational wave maps on a wormhole

**Int. Math. Res. Not. IMRN**, 15 (2019), p. 4603-4706. - Soliton resolution for equivariant wave maps on a wormhole

**Comm. Math. Phys.**359 (2018), p. 375-426. - Scattering for radial energy-subcritical wave equations in dimensions 4 and 5

**Comm. Partial Differential Equations**, 42 (2017), p. 852-894. - Profiles for the radial focusing energy-critical wave equation in odd dimensions

**Adv. Differential Equ.**, 21 (2016), p. 505-570. - A partial data result for less regular conductivities in admissible geometries

**Inverse Probl. Imag.**, 10 (2016), p. 247-262.