Weak Solutions and Their Kinetic Energy Regarding Time-Periodic Navier–Stokes Equations in Three Dimensional Whole-Space

PERIODIC SOLUTIONS OF CERTAIN THREE DIMENSIONAL AUTONOMOUS SYSTEMS

There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...

On Some Classes of Time-Periodic Solutions for the Navier-Stokes Equations in the Whole Space

For the 3D Navier–Stokes problem on the whole space, we study existence, regularity and stability of time-periodic solutions in Lebesgue, Lorentz or Sobolev spaces, when the periodic forcing belongs to critical classes of forces.

Existence of Time-periodic Solutions to Incompressible Navier-stokes Equations in the Whole Space

In this article, we assume that the force field acting over a fluid is periodic on time and the velocity of the liquid is zero at spatial infinity. We prove the existence of time-periodic solutions to the system governing the motion of an incompressible fluid filling the whole space.

Time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space with a drift term: Asymptotic profile at spatial infinity

periodic solutions of certain three dimensional autonomous systems

there has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. the popular poincare-bendixon theorem applies well to the former but not the latter (see [2] and [3]). we give a necessary condition for the existence of periodic solutions for the third order autonomous systems, t...