28,029 research outputs found
A criterion for the existence of strong solutions for the 3D Navier-Stokes equations
No full textIn this note we provide a criterion for the existence of globally defined solutions for any regular initial data for the 3D Navier–Stokes system in Serrin’s classes
Regularity of Weak Solutions and Their Attractors for a Parabolic Feedback Control Problem
No full textAbstract We investigate additional regularity properties of all globally defined
weak solutions, their global and trajectory attractors for a class of autonomous
differential inclusion with upper semi-continuous interaction function, when initial
data uτ ∈ L2(). The main contributions of this paper are: (i) additional regularity
and new topological properties of all weak solutions of parabolic feedback control
problem with upper semi-continuous interaction function, (ii) a sufficient condition
for regularity of global and trajectory attractors, and (iii) new a priory estimates for
all weak solutions
Local subdifferentials and multivariational inequalities in Banach and Frechet spaces
No full textSome functional-topological concepts of subdifferential and locally subdifferential maps in Frechet spaces are established. Multivariational inequalities with an operator of the pseudo-monotone type, connected with subdifferential maps, are considered
On some approximations and main topological descriptions for special classes of Frechet spaces with integrable derivatives
No full textOn some approximations and main topological descritions for special classes of Banach spaces with integrable derivatives
No full textMultivalued penalty method for evolution variational inequalities with λ0-pseudomonotone multivalued maps
No full textWe consider evolution variational inequalities with λ 0-pseudomonotone maps. The main properties of these maps are investigated. By using the finite-difference method, we prove the property of strong solvability for the class of evolution variational inequalities with λ 0-pseudomonotone maps. Using the penalty method for multivalued maps, we show the existence of weak solutions of evolution variational inequalities on closed convex sets. The class of multivalued penalty operators is constructed. We also consider a model example to illustrate this theory
Method of approximation of evolutionary inclusions and variational inequalities by stationary
No full textTopological properties of strong solutions for the 3D Navier-Stokes equations
No full textIn this chapter we give a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial dat
Uniform Global Attractor for a Class of Nonautonomous Evolution Hemivariational Inequalities with Multidimensional “Reaction-Velocity” Law
No full textWe consider non-autonomous evolution inclusions and hemivariation inequalities with possibly non-monotone multidimensional “reaction-velocity” law. The dynamics of all weak solutions defined on the positive semi-axis of time is investigated. We prove the existence global attractor. New properties of complete trajectories are justified. The pointwise behavior of such problem solutions on attractor is described in the autonomous case
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