On regularity of stationary solutions to the Navier-Stokes equation in 3D torus.
On representations of Lie algebras of a generalized Tavis-Cummings model.
On Schrödinger maps from to
We prove an estimate for the difference of two solutions of the Schrödinger map equation for maps from to This estimate yields some continuity properties of the flow map for the topology of , provided one takes its quotient by the continuous group action of given by translations. We also prove that without taking this quotient, for any the flow map at time is discontinuous as a map from , equipped with the weak topology of to the space of distributions The argument relies in an essential...
On second-grade fluids with vanishing viscosity.
On shape optimization problems involving the fractional laplacian
Our concern is the computation of optimal shapes in problems involving (−Δ)1/2. We focus on the energy J(Ω) associated to the solution uΩ of the basic Dirichlet problem ( − Δ)1/2uΩ = 1 in Ω, u = 0 in Ωc. We show that regular minimizers Ω of this energy under a volume constraint are disks. Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the moving plane method.
On similarity solution of a boundary layer problem for power-law fluids
The boundary layer equations for the non-Newtonian power law fluid are examined under the classical conditions of uniform flow past a semi infinite flat plate. We investigate the behavior of the similarity solution and employing the Crocco-like transformation we establish the power series representation of the solution near the plate.
On singularities of capillary surfaces in the absence of gravity.
On singularities of solutions to the Dirichlet problem of hydrodynamics near the vertex of a cone.
On Solutions of the Initial Value Problem for the Nonlinear Schrödinger Equations in One Space Dimension.
On solutions of the KZ and qKZ equations at level zero
On solvability of fourth order operator-diferential equations of elliptic type on weight spaces.
On solvability of the Stokes problem in Sobolev power weight spaces
On some Boussinesq systems in two space dimensions: theory and numerical analysis
A three-parameter family of Boussinesq type systems in two space dimensions is considered. These systems approximate the three-dimensional Euler equations, and consist of three nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. For a subset of these systems it is proved that their Cauchy problem is locally well-posed in suitable Sobolev classes. Further, a class of these systems is discretized...
On some free boundary problems for Navier-Stokes equations
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 some free boundary problems for the Navier-Stokes equations with moving contact points and lines.
On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations
In this paper, we propose implicit and semi-implicit in time finite volume schemes for the barotropic Euler equations (hence, as a particular case, for the shallow water equations) and for the full Euler equations, based on staggered discretizations. For structured meshes, we use the MAC finite volume scheme, and, for general mixed quadrangular/hexahedral and simplicial meshes, we use the discrete unknowns of the Rannacher−Turek or Crouzeix−Raviart finite elements. We first show that a solution...
On some inequalities for solutions of equations describing the motion of a viscous compressible heat-conducting capillary fluid bounded by a free surface
We derive inequalities for a local solution of a free boundary problem for a viscous compressible heat-conducting capillary fluid. The inequalities are crucial in proving the global existence of solutions belonging to certain anisotropic Sobolev-Slobodetskii space and close to an equilibrium state.
On some properties of solutions of transonic potential flow problems
The paper deals with solutions of transonic potential flow problems handled in the weak form or as variational inequalities. Using suitable generalized methods, which are well known for elliptic partial differential equations of the second order, some properties of these solutions are derived. A maximum principle, a comparison principle and some conclusions from both ones can be established.
On some properties of the solution of the differential equation
In the paper it is shown that each solution ot the initial value problem (2), (3) has a finite limit for , and an asymptotic formula for the nontrivial solution tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions , .
On some Schroedinger-type variational inequalities