TAKADA, Ryo

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Title
Associate Professor
Field
Partial Differential Equations
Research interests
Mathematical analysis of nonlinear partial differential equations arising in fluid dynamics
Current research

The subject of my research is mathematical analysis of nonlinear partial differential equations arising in fluid dynamics. In particular, I have investigated the well-posedness problem of the Euler equations, the Navier-Stokes equations and the Boussinesq equations, and studied the stability and asymptotics of their solutions. My recent research interest is the mathematical analysis of dispersion and anisotropy in the rotating stably stratified fluids.

Selected publications
  1. R. Takada, Counterexamples of commutator estimates in the Besov and the Triebel-Lizorkin space related to the Euler equations, SIAM. J. Math. Anal. 42 (2010), 2473--2483.
  2. O. Sawada and R. Takada, On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity, J. Funct. Anal. 260 (2011), 2148--2162.
  3. T. Iwabuchi and R. Takada, Global solutions for the Navier-Stokes equations in the rotational framework, Math. Ann. 357 (2013), 727--741.
  4. Y. Koh, S. Lee and R. Takada, Strichartz estimates for the Euler equations in the rotational framework, J. Differential Equations 256 (2014), 707--744.
  5. S. Lee and R. Takada, Dispersive estimates for the stably stratified Boussinesq equations, Indiana Univ. Math. J. 66 (2017), 2037--2070.
  6. R. Takada, Strongly stratified limit for the 3D inviscid Boussinesq equations, Arch. Ration. Mech. Anal. 232 (2019), 1475--1503.
  7. H. Ohyama and R. Takada, Asymptotic limit of fast rotation for the incompressible Navier-Stokes equations in a 3D layer, J. Evol. Equ. 21 (2021), 2591--2629.

Memberships, Awards and

activities

The Mathematical Society of Japan

MSJ Takebe Katahiro Prize for Encouragement of Young Researchers 2012