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Ryo TAKADA Last modified date:2019.06.11



Graduate School
Undergraduate School


E-Mail
Academic Degree
Doctor of Science
Field of Specialization
Partial Differential Equations, Harmonic Analysis
Outline Activities
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.
Research
Research Interests
  • Partial Differential Equations
    keyword : Partial Differential Equations
    2007.04.
Academic Activities
Papers
1. Ryo Takada, Strongly stratified limit for the 3D inviscid Boussinesq equations, Arch. Ration. Mech. Anal., 232, 1475-1503, 2019.03, We consider the initial value problem of the 3D inviscid Boussinesq equations for stably stratified fluids. We prove the long time existence of classical solutions for large initial data when the buoyancy frequency is sufficiently high. Furthermore, we consider the singular limit of the strong stratification, and show that the long time classical solution converges to that of 2D incompressible Euler equations in some space-time Strichartz norms..
2. Sanghyuk Lee, Ryo Takada, Dispersive estimates for the stably stratified Boussinesq equations, Indiana Univ. Math. J., 66, 2037-2070, 2017.12, We consider the initial value problem for the 3D Boussinesq equations for stably stratified fluids without the rotational effect. We establish the sharp dispersive estimate for the linear propagator related to the stable stratification. As an application, we give the explicit relation between the size of initial data and the buoyancy frequency which ensures the unique existence of global solutions to our system. In particular, it is shown that the size of the initial thermal disturbance can be taken in proportion to the strength of stratification..
3. Youngwoo Koh, Sanghyuk Lee, Ryo Takada, Strichartz estimates for the Euler equations in the rotational framework, J. Differential Equations, 10.1016/j.jde.2013.09.017, 256, 2, 707-744, 2014.01.
4. Ryo Takada, Counterexamples of commutator estimates in the Besov and the Triebel-Lizorkin space related to the Euler equations, SIAM. J. Math. Anal., 10.1137/100782498, 42, 2473-2483, 2010.10.
Presentations
1. Ryo Takada, Time periodic initial value problem for rotating stably stratified fluids, Geophysical Fluid Dynamics, Oberwolfach, 2017.05, Consider the 3D incompressible Boussineq equations for rotating stably stratified fluids.
It is shown that this set of equations possesses a unique time periodic or almost time periodic solutions for external forces satisfying these properties, which, however, do not necessarily need to be small.
An explicit bound on the size of the external force, depending on the buoyancy frequency N, is given, which then allows for the unique existence of time periodic or almost periodic solutions.
In particular, the size of the external forces can be taken large with respect to the buoyancy frequency.
The approach depends crucially on the dispersive effect of the rotation and the stable stratification..
2. Ryo Takada, Long time solvability for the 3D rotating Euler equations, VORTICITY, ROTATION AND SYMMETRY (III) - Approaching Limiting Cases of Fluid Flows, Luminy, 2014.05.
3. Ryo Takada, Dispersive estimates for the Euler and the Navier-Stokes equations with the Coriolis force, Geophysical Fluid Dynamics, Oberwolfach, 2013.02.
Membership in Academic Society
  • The Mathematical Society of Japan