Recent Publications

1. K. Ohkitani,
   "Dynamical equation for velocity potentials in incompressible irrotational Euler flows with singular vorticity distributions : a refinement of Bernoulli theorem," Phys. Rev. E 92, 033010 (2015).
2. K. Ohkitani,
   "Study of the Navier-Stokes regularity problem with critical norms", Fluid. Dyn. Res. 48, 021401(2016).
3. K. Ohkitani,
   "Late formation of singularities in solutions to the Navier-Stokes equations," J. Phys. A: Math. Theor. 49, 015502 (2016).
4. K. Ohkitani,
   "Characterization of blowup for the Navier-Stokes equations using vector potentials," AIP Advances 7, 015211 (2017).
5. K. Ohkitani,
   "Near-invariance under dynamic scaling for the Navier-Stokes equations in critical spaces: a probabilistic approach to regularity problems," J. Phys. A: Math. Theor. 50 (2017) 045501.
6. K. Ohkitani,
   "Analogue of the Cole-Hopf transform for the incompressible Navier-Stokes equations and its application," Journal of Turbulence, 18 (2017), 465--479.
7. K. Ohkitani,
   "Cole-Hopf--Feynman-Kac formula and quasi-invariance for Navier-Stokes equations," J. Phys. A: Math. Theor. 50 (2017) 405501.
8. K. Ohkitani,
   "Study of the Euler equations by Clebsch potentials," Nonlinearity, 31 (2018) R25-R51.
9. R. Vanon and K. Ohkitani,
   "Applications of a Cole-Hopf transform to the 3D Navier-Stokes equations," J. Turbulence 19 (2018) 1--12.
10. K. Ohkitani,
    "Quasi-invariance for the Navier-Stokes equations," in 'Partial Differenatial Equations and Fluid Mechanics,' LMS Lecture Notes Series 452, Cambridge University Press. ed. C. Fefferman, J.C. Robinson, and J.L. Rodrigo (2018).
11. K. Ohkitani,
    "Study of the Hopf functional equation for turbulence: Duhamel principle and dynamical scaling," Phys. Rev. E 101 (2020) 013104.
12. K. Ohkitani and R. Vanon,
    "Self-similar source-type solutions to the three-dimensional Navier-Stokes equations," Proc. R. Soc. A478 (2022) 20210527
13. K. Ohkitani,
    "Remarks on the principles of statistical fluid mechanics," Phil. Trans. R. Soc. A380(2022) 20210077
14. K. Ohkitani,
    "Self-similarity in turbulence and its applications," Phil. Trans. R. Soc. A380 (2022) 20210048
15. K. Ohkitani,
    "Self-similar solutions to the hypoviscous Burgers and SQG equations at criticality," J. Phys. A: Math. Theor. 56 (2023) 275204.
16. K. Ohkitani,
    "Numerical comparison of two-dimensional Navier-Stokes flows on the whole plane and the periodic domain," Phys. Rev. Fluids 8, 124607 (2023).
17. K. Ohkitani,
    "Numerical study on how advection delays and removes singularity formation in the Navier-Stokes equations," Nonlinearity 37 (2024) 055002.
18. K. Ohkitani,
    "Generalized incompressible fluid dynamical system interpolating between the Navier-Stokes and Burgers equations in two dimensions," J. Phys. A: Math. Theor. (2025), to appear.