Abstract We consider the local existence and uniqueness of solutions for a system consisting an inviscid fluid with free boundary, modeled by Euler equations, in domain enclosed elastic which evolves according to wave equation. derive priori estimates also conclude uniqueness. Both, are obtained under assumption that data belongs $$H^{r}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML...

We investigate the dynamics of membranes that are held by freely-rotating rigid tethers in fluid flows. The tethered boundary condition allows periodic and chaotic oscillatory motions for certain parameter values. characterize oscillations terms deflection amplitudes, dominant periods, numbers local extrema along across space membrane mass density, stretching modulus, pretension, tether length....

The stability of modulated atmospheric flows is analyzed. The equations govern. ing the disturbance motion are solved by Galerkin expansions with time-dependent coefficients. Asymptotic stability bounds are then established by constructing Liapuno"\ functions for the resulting differential systems.

ABSTRACT. It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space B 3,∞. When the singular set of the solution is (or belongs to) a smooth manifold, we derive various L-space regularity criteria dimensionally equivalent to the critical one. In particular, if the singular set is a hypersurface the energy of u is conser...

We prove that any steady solution to the Cω Euler equations on a Riemannian S3 must possess a periodic orbit bounding an embedded disc. One key ingredient is an extension of Fomenko’s work on the topology of integrable Hamiltonian systems to a degenerate case involving stratified integrals. The result on the Euler equations follows from this when combined with some contact-topological perspecti...

In the context of an airship development programme, inviscid flow behavior and its coupling with structure flexibility are investigated. For this purpose, we have chosen a nonlinear analysis tool relying on the unsteady Euler model for the flow part and the classical elastodynamic equations for the structure. The numerical model for the flow is based on a Mixed Element Volume discretization der...

We give lower bounds for the lifespan of a solution to the inviscid Boussinesq system. In dimension two, we point out that it tends to infinity when the initial (relative) temperature tends to zero. This is, to the best of our knowledge, the first result of this kind for the inviscid Boussinesq system. In passing, we provide continuation criteria (of independent interest) in the N -dimensional ...

We develop variational principles to study the structure and the stability of equilibrium states of axisymmetric flows. We show that the axisymmetric Euler equations for inviscid flows admit an infinite number of steady state solutions. We find their general form and provide analytical solutions in some special cases. The system can be trapped in one of these steady states as a result of an inv...