# Strichartz estimates for the Euler equations in the rotational framework

@article{Koh2014StrichartzEF, title={Strichartz estimates for the Euler equations in the rotational framework}, author={Youngwoo Koh and Sanghyuk Lee and Ryo Takada}, journal={Journal of Differential Equations}, year={2014}, volume={256}, pages={707-744} }

## 29 Citations

Long time existence of classical solutions for the 3D incompressible rotating Euler equations

- Mathematics
- 2016

We consider the initial value problem of the 3D incompressible rotating Euler equations. We prove the long time existence of classical solutions for initial data in H(R) with s > 5/2. Also, we give…

Global solutions for the incompressible rotating stably stratified fluids

- Mathematics
- 2017

We consider the initial value problem of the 3D incompressible Boussinesq equations for rotating stratified fluids. We establish the dispersive and the Strichartz estimates for the linear propagator…

A remark on a priori estimate for the Navier-Stokes equations with the Coriolis force

- Mathematics
- 2015

The Cauchy problem for the Navier-Stokes equations with the Coriolis force is considered. It is proved that a similar a priori estimate, which is derived for the Navier-Stokes equations by Lei and…

Decay estimate and well-posedness for the 3D Euler equations with Coriolis force

- Mathematics
- 2018

In this paper, we are concerned with the cauchy problem of the 3D Euler equations in rotation framework. Provided the speed of rotation $$|\Omega |$$|Ω| is sufficiently large, we can obtain the…

On the 3D Euler equations with Coriolis force in borderline Besov spaces

- Mathematics
- 2017

We consider the 3D Euler equations with Coriolis force (EC) in the whole space. We show long-time solvability in Besov spaces for high speed of rotation $\Omega $ and arbitrary initial data. For…

Strongly Stratified Limit for the 3D Inviscid Boussinesq Equations

- MathematicsArchive for Rational Mechanics and Analysis
- 2018

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…

Coriolis effect on temporal decay rates of global solutions to the fractional Navier–Stokes equations

- Mathematics
- 2021

The incompressible fractional Navier–Stokes equations in the rotational framework is considered. We establish the global existence result and temporal decay estimate for a unique smooth solution when…

Global Axisymmetric Euler Flows with Rotation

- Mathematics
- 2021

We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform “rigid body” rotation. These solutions are axisymmetric, of Sobolev…

On the stabilizing effect of rotation in the 3d Euler equations

- Mathematics
- 2020

While it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More…

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