On the general relativistic magnetohydrodynamics with a generalized thermodynamical differential equation
On the geometrical structure of shock waves in general relativity
On the geometry of the relativistic electromagnetic fluid flows
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 stability of contact discontinuity for compressible Navier-Stokes equations
On the global wellposedness of the 3-D Navier–Stokes equations with large initial data
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 ground states of vector nonlinear Schrödinger equations
On the heat impulse method for deducing sap flow.
On the Height of a Capillary Surface.
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...
On the inequalities associated with a model of Graffi for the motion of a mixture of two viscous, incompressible fluids
We demonstrate a theorem of existence and uniqueness on a large scale of the solution of a system of differential disequations associated to a Graffi model relative to the motion of two incompressible viscous fluids.
On the instability of solitary-wave solutions for fifth-order water wave models.
On the instantaneous spreading for the Navier–Stokes system in the whole space
We consider the spatial behavior of the velocity field of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of . We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space
We consider the spatial behavior of the velocity field u(x, t) of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of u. We also give some new examples of solutions which have a stronger spatial localization than in the generic case.