

Title

Associate Professor 
Field

Mathematical Fluid Dynamics 
Research interests

Mathematical analysis of fluid mechanics by using the NavierStokes
and Euler equations

Current research

My recent research interest is mathematical turbulence, in particular,
to clarify the relation between ``zeroth law" and
``vortexstretching". Zeroth law is the cornerstone of turbulence,
especially, origin of the Onsager conjecture. To the best of my
knowledge, up to now, nothing was known about the zeroth law itself in
mathematics. I would explain our recent result (with Prof. InJee
Jeong) in the following:
We prepared smallscale vortex blob and largescale antiparallel
vortex tubes for the initial data, and showed that the corresponding
3D Euler flow creates instantaneous vortexstretching. In turn, using
this stretching, we showed that the corresponding 3D NavierStokes
flow satisfies a modified version of zerothlaw, which is the
cornerstone of the turbulence study field. Thus this instantaneous
vortexstretching could be a key to make further progress in this
field. We conjecture that an initial data which satisfies the actual
zerothlaw should behave as in GotoSaitoKawahara's turbulence
picture (2017). In the Appendix, we mathematically formulated their
turbulence picture and proved Kolmogorov's $5/3$law, by assuming
spacelocality, scalelocality, energy flux in equilibrium state and
spacefilling (Frisch 1995).

Selected publications

 I.J. Jeong and T. Yoneda, A remark on the zeroth law and
instantaneous vortex stretching on the incompressible 3D Euler
equations, submitted.
 G. Misiolek and T. Yoneda, Continuity of the solution map of the Euler
equations in H\"older spaces and weak norm inflation in Besov spaces,
Trans. Amer. Math. Soc. 370 (2018), 47094730.
 N. Kishimoto and T. Yoneda, Global solvability of the rotating
NavierStokes equations with fractional Laplacian in a periodic
domain, Math. Ann. 372 (2018) 743779.
 PY. Hsu, H. Notsu, T. Yoneda, A local analysis of the axisymmetric
NavierStokes flow near a saddle point and noslip flat boundary, J.
Fluid Mech. 794 (2016) 444459.
 M. Yamada and T. Yoneda, Resonant interaction of Rossby waves in
twodimensional flow on a β plane, Physica D, 245 (2013) 17.
 T. Yoneda, Longtime solvability of the NavierStokes equations in a
rotating frame with spatially almost periodic large data, Arch.
Ration. Mech. Anal., 200 (2011) 225237.
 T. Yoneda, Illposedness of the 3DNavierStokes equations in a
generalized Besov space near BMO^{1}, J. Funct. Anal., 258 (2010)
33763387.

Memberships, activities and
Awards

The Mathematical Society of Japan
2014：The Commendation for Science and Technology by the Minister of
Education, Culture, Sports, Science and Technology:The Young Scientists'
Prize.
2012：MSJ Tatebe Katahiro Prize.
2012：Inoue Research Award for Young Scientists.
2009: Chairman Award for Outstanding Ingenuity and Creativity, University
of Tokyo.
