On the convergence rate of spectral approximation for the equations for nonhomogeneous asymmetric fluids
On the derivation of homogeneous hydrostatic equations
On the derivation of homogeneous hydrostatic equations
In this paper we study the derivation of homogeneous hydrostatic equations starting from 2D Euler equations, following for instance [2,9]. We give a convergence result for convex profiles and a divergence result for a particular inflexion profile.
On the differential system governing flows in magnetic field with data in .
On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model
We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term ɛΔ3. We establish the global existence, uniqueness, and regularity of solutions. Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of ɛ > 0.
On the Dirac delta as initial condition for nonlinear Schrödinger equations
On the equations of ideal incompressible magneto-hydrodynamics
On the evolution equations of viscous gaseous stars
On the existence of weak solutions for the initial-boundary value problem in the Jeffreys model of motion of a viscoelastic medium.
On the exterior problem in 2D for stationary flows of fluids with shear dependent viscosity
On the complement of the unit disk we consider solutions of the equations describing the stationary flow of an incompressible fluid with shear dependent viscosity. We show that the velocity field is equal to zero provided and uniformly. For slow flows the latter condition can be replaced by uniformly. In particular, these results hold for the classical Navier-Stokes case.
On the exterior steady problem for the equations of a viscous isothermal gas
We prove existence and a representation formula for solutions to the equations describing steady flows of an isothermal, viscous, compressible gas having a positive infimum for the density , moving in an exterior domain, when the speed of the obstacle and the external forces are sufficiently small.
On the global existence for a regularized model of viscoelastic non-Newtonian fluid
We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like (p > 6/5), regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we prove global existence of a weak solution to the corresponding system of partial differential equations.
On the global existence for the axisymmetric Euler equations
This paper deals with the global well-posedness of the D axisymmetric Euler equations for initial data lying in critical Besov spaces . In this case the BKM criterion is not known to be valid and to circumvent this difficulty we use a new decomposition of the vorticity .
On the global existence for the Muskat problem
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an maximum principle, in the form of a new “log” conservation law which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance . Previous results of this...
On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting capillary fluid.
On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid
We consider the motion of a viscous compressible heat conducting fluid in ℝ³ bounded by a free surface which is under constant exterior pressure. Assuming that the initial velocity is sufficiently small, the initial density and the initial temperature are close to constants, the external force, the heat sources and the heat flow vanish, we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.
On the global regularity of -dimensional generalized Boussinesq system
We study the -dimensional Boussinesq system with dissipation and diffusion generalized in terms of fractional Laplacians. In particular, we show that given the critical dissipation, a solution pair remains smooth for all time even with zero diffusivity. In the supercritical case, we obtain component reduction results of regularity criteria and smallness conditions for the global regularity in dimensions two and three.
On the global regularity of subcritical Euler–Poisson equations with pressure
We prove that the one-dimensional Euler–Poisson system driven by the Poisson forcing together with the usual -law pressure, , admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the -system. Global regularity is shown to depend on whether or not the initial configuration of the Riemann...
On the global well-posedness of the Boussinesq system with zero viscosity
In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.
On the importance of solid deformations in convection-dominated liquid/solid phase change of pure materials
We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well-known and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid phase to the...