The existence and uniqueness of solutions of equations for ideal compressible polytropic fluids.
The existence of an exponential attractor in magneto-micropolar fluid flow via the ℓ-trajectories method
We consider the magneto-micropolar fluid flow in a bounded domain Ω ⊂ ℝ². The flow is modelled by a system of PDEs, a generalisation of the two-dimensional Navier-Stokes equations. Using the Galerkin method we prove the existence and uniqueness of weak solutions and then using the ℓ-trajectories method we prove the existence of the exponential attractor in the dynamical system associated with the model.
The far-field modelling of transonic compressible flows
We present a method for the construction of artificial far-field boundary conditions for two- and three-dimensional exterior compressible viscous flows in aerodynamics. Since at some distance to the surrounded body (e.g. aeroplane, wing section, etc.) the convective forces are strongly dominant over the viscous ones, the viscosity effects are neglected there and the flow is assumed to be inviscid. Accordingly, we consider two different model zones leading to a decomposition of the original flow...
The finite element method with nodes moving along the characteristics for convection-diffusion equations.
The fundamental solution of a modified Oseen problem.
The initial value problem for the equations of magnetohydrodynamic type in non-cylindrical domains.
By using the spectral Galerkin method, we prove the existence of weak solutions for a system of equations of magnetohydrodynamic type in non-cylindrical domains.
The initial-boundary value problem with a free surface condition for the -approximations of the Navier-Stokes equations and some their regularizations
The inviscid limit for density-dependent incompressible fluids
This paper is devoted to the study of smooth flows of density-dependent fluids in or in the torus . We aim at extending several classical results for the standard Euler or Navier-Stokes equations, to this new framework.Existence and uniqueness is stated on a time interval independent of the viscosity when goes to . A blow-up criterion involving the norm of vorticity in is also proved. Besides, we show that if the density-dependent Euler equations have a smooth solution on a given time...
The mathematical theory of low Mach number flows
The mathematical theory of the passage from compressible to incompressible fluid flow is reviewed.
The mathematical theory of low Mach number flows
The mathematical theory of the passage from compressible to incompressible fluid flow is reviewed.
The mathematics of suspensions: Kac walks and asymptotic analyticity.
The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section
We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [J. Math. Pures Appl.74 (1995) 483–548]. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a class...
The modulational regime of three-dimensional water waves and the Davey-Stewartson system
The motion of the free surface of a liquid
The penalty method for the equations of viscoelastic media
The Penetrable sphere with a soft Eccentric core within an Accoustic wave field
The problem of data assimilation for soil water movement
The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
The problem of data assimilation for soil water movement
The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
The pseudospectral method for thermotropic primitive equation and its error estimation.
The pullback attractors for the nonautonomous Camassa-Holm equations.