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On recent progress for the stochastic Navier Stokes equations

Jonathan Mattingly (2003)

Journées équations aux dérivées partielles

We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations. Since our desire is to make the core ideas clear, we will mostly work with a specific example : the stochastically forced Navier Stokes equations. To further clarify ideas, we will also examine in detail a toy problem. A few general theorems are given. Spatial regularity, ergodicity, exponential...

On some free boundary problems for Navier-Stokes equations

Ewa Zadrzyńska (2005)

Banach Center Publications

In this survey we report on existence results for some free boundary problems for equations describing motions of both incompressible and compressible viscous fluids. We also present ways of controlling free boundaries in two cases: a) when the free boundary is governed by surface tension, b) when surface tension does not occur.

On the blow up criterion for the 2-D compressible Navier-Stokes equations

Lingyu Jiang, Yidong Wang (2010)

Czechoslovak Mathematical Journal

Motivated by [10], we prove that the upper bound of the density function ρ controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.

On the controllability of the Burger equation

T. Horsin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We present here a return method to describe some attainable sets on an interval of the classical Burger equation by means of the variation of the domain.

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