My research is primarily in the study of partial differential equations and continuum mechanics.

Publications

• Special Cosserat rods with rate-dependent evolving natural configurations
  (with K. R. Rajagopal)
  Int. J. Eng. Sci., to appear.
• Elastic solids with strain-gradient elastic boundary surfaces
  Preprint, 2023.
• 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.
• On evolving natural curvature for an inextensible, unshearable, viscoelastic rod 
  (with K. R. Rajagopal)
  J. Elast., to appear.
• Longitudinal shock waves in a class of semi-infinite stretch-limited elastic strings
  Math. Mech. Solids, 27 (2022), p. 474–490. 
• 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.
• Dynamics of bubbling wave maps with prescribed radiation (with J. Jendrej, A. Lawrie)
  Ann. Sci. de l’ENS., (4) 55 (2022), p. 1135-1198.
• 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 equivariant wave maps on a wormhole
  Comm. Math. Phys. 359 (2018), p. 375-426.
• Soliton resolution for corotational wave maps on a wormhole
  Int. Math. Res. Not. IMRN, 15 (2019), p. 4603-4706.
• 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.