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 dimension of the pullback attractors for -Navier-Stokes equations.
On the Dirac delta as initial condition for nonlinear Schrödinger equations
On the double-well problem for Dirac operators
On the energy critical focusing non-linear wave equation
On the equation of a rotating film.
On the equations of ideal incompressible magneto-hydrodynamics
On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account.
On the Euler equations of incompressible perfect fluids
On the Euler equations with a singular external velocity field
On the evolution equations of viscous gaseous stars
On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion
This paper is devoted to the study of the incompressible Navier-Stokes equations with mass diffusion in a bounded domain in R³ with C³ boundary. We prove the existence of weak solutions, in the large, and the behavior of the solutions as the diffusion parameter λ → 0. Moreover, the existence of L²-strong solution, in the small, and in the large for small data, is proved. Asymptotic regularity (the regularity after a finite period) of a weak solution is studied. Finally, using the Dore-Venni theory,...
On the Existence and Uniqueness of Non-homogeneous Motions in Exterior Domains.
On the existence for the Cauchy-Neumann problem for the Stokes system in the -framework
The existence for the Cauchy-Neumann problem for the Stokes system in a bounded domain is proved in a class such that the velocity belongs to , where r > 3. The proof is divided into three steps. First, the existence of solutions is proved in a half-space for vanishing initial data by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing initial data is considered....
On the existence for the Dirichlet problem for the compressible linearized Navier-Stokes system in the -framework
The existence of solutions to the Dirichlet problem for the compressible linearized Navier-Stokes system is proved in a class such that the velocity vector belongs to with r > 3. The proof is done in two steps. First the existence for local problems with constant coefficients is proved by applying the Fourier transform. Next by applying the regularizer technique the existence in a bounded domain is shown.
On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.
On the existence of pullback attractor for a two-dimensional shear flow with Tresca's boundary condition
We consider a two-dimensional Navier-Stokes shear flow with time dependent boundary driving and subject to Tresca law. We establish the existence of a unique global in time solution and then, using a recent method based on the concept of the Kuratowski measure of noncompactness of a bounded set, we prove the existence of the pullback attractor for the associated cocycle. This research is motivated by a problem from lubrication theory.
On the existence of solutions for the nonstationary Stokes system with slip boundary conditions in general Sobolev-Slobodetskii and Besov spaces
We prove the existence of solutions to the evolutionary Stokes system in a bounded domain Ω ⊂ ℝ³. The main result shows that the velocity belongs either to or to with p > 3 and s ∈ ℝ₊ ∪ 0. The proof is divided into two steps. First the existence in for k ∈ ℕ is proved. Next applying interpolation theory the existence in Besov spaces in a half space is shown. Finally the technique of regularizers implies the existence in a bounded domain. The result is generalized to the spaces and with...
On the existence of stationary solutions to compressible Navier-Stokes equations