111 research outputs found
Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data
We investigate large time existence of solutions of the
Navier-Stokes-Boussinesq equations with spatially almost periodic large data
when the density stratification is sufficiently large. In 1996, Kimura and
Herring \cite{KH} examined numerical simulations to show a stabilizing effect
due to the stratification. They observed scattered two-dimensional
pancake-shaped vortex patches lying almost in the horizontal plane. Our result
is a mathematical justification of the presence of such two-dimensional
pancakes. To show the existence of solutions for large times, we use
-norm of amplitudes. Existence for large times is then proven using
techniques of fast singular oscillating limits and bootstrapping argument from
a global-in-time unique solution of the system of limit equations
Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary Growth
We derive a uniform exponential decay of the total energy for the nonlinear
Klein-Gordon equation with a damping around spatial infinity in the whole space
or in the exterior of a star shaped obstacle
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