## YONEDA, Tsuyoshi

 Title Associate Professor Field Mathematical Fluid Dynamics Research interests Mathematical analysis of fluid mechanics by using the Navier-Stokes and Euler equations Current research My recent research interest is mathematical turbulence, in particular, to clarify the relation between zeroth law" and vortex-stretching". 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. In-Jee Jeong) in the following: We prepared small-scale vortex blob and large-scale anti-parallel vortex tubes for the initial data, and showed that the corresponding 3D Euler flow creates instantaneous vortex-stretching. In turn, using this stretching, we showed that the corresponding 3D Navier-Stokes flow satisfies a modified version of zeroth-law, which is the cornerstone of the turbulence study field. Thus this instantaneous vortex-stretching could be a key to make further progress in this field. We conjecture that an initial data which satisfies the actual zeroth-law should behave as in Goto-Saito-Kawahara's turbulence picture (2017). In the Appendix, we mathematically formulated their turbulence picture and proved Kolmogorov's $-5/3$-law, by assuming space-locality, scale-locality, energy flux in equilibrium state and space-filling (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), 4709-4730. N. Kishimoto and T. Yoneda, Global solvability of the rotating Navier-Stokes equations with fractional Laplacian in a periodic domain, Math. Ann. 372 (2018) 743-779. P-Y. Hsu, H. Notsu, T. Yoneda, A local analysis of the axi-symmetric Navier-Stokes flow near a saddle point and no-slip flat boundary, J. Fluid Mech. 794 (2016) 444-459. M. Yamada and T. Yoneda, Resonant interaction of Rossby waves in two-dimensional flow on a β plane, Physica D, 245 (2013) 1--7. T. Yoneda, Long-time solvability of the Navier-Stokes equations in a rotating frame with spatially almost periodic large data, Arch. Ration. Mech. Anal., 200 (2011) 225--237. T. Yoneda, Ill-posedness of the 3D-Navier-Stokes equations in a generalized Besov space near BMO^{-1}, J. Funct. Anal., 258 (2010) 3376--3387. 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.