Interior regularity for the quasilinear elliptic systems with nonsmooth coefficients
Interior regularity for weak solutions of nonlinear second order elliptic systems
Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case
In this paper we consider weak solutions to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain ( or ). For the critical case we prove the higher integrability of which forms the basis for applying the method of differences in order to get fractional differentiability of . From this we show the existence of second order weak derivatives of .
Interior regularity of weak solutions to the perturbed Navier-Stokes equations
In this paper we establish interior regularity for weak solutions and partial regularity for suitable weak solutions of the perturbed Navier-Stokes system, which can be regarded as generalizations of the results in L. Caffarelli, R. Kohn, L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations, Commun. Pure. Appl. Math. 35 (1982), 771–831, and S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations, Manuscr. Math. 69...
Intermittency on catalysts: symmetric exclusion.
Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics
We investigate the existence, uniqueness and polynomial stability of the weighted pseudo almost automorphic solutions to a class of linear and semilinear parabolic evolution equations. The necessary tools here are interpolation spaces and interpolation theorems which help to prove the boundedness of solution operators in appropriate spaces for linear equations. Then for the semilinear equations the fixed point arguments are used to obtain the existence and stability of the weighted pseudo almost...
Introduction
Invariance of the Gibbs measure for the Benjamin–Ono equation
In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than , extending the well-posedness result of Molinet [20].
Invariant manifolds and almost automorphic solutions of second-order monotone equations
Invariant manifolds for one-dimensional parabolic partial differential equations of second order
Invariant measures and long-time behavior for the Benjamin-Ono equation
We summarize the main ideas in a series of papers ([20], [21], [22], [5]) devoted to the construction of invariant measures and to the long-time behavior of solutions of the periodic Benjamin-Ono equation.
Invariant measures for Burgers equation with stochastic forcing.
Invariant measures for the defocusing Nonlinear Schrödinger equation
We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane . We also prove an estimate giving some intuition to what may happen in dimensions.
Invariant Rectangles and Strongly Coupled Semilinear Parabolic.
Invariant regions and global existence of solutions for reaction-diffusion systems with a tridiagonal matrix of diffusion coefficients and nonhomogeneous boundary conditions.
Invariant regions associated with quasilinear damped wave equations
Invariant sets for nonlinear evolution equations, Cauchy problems and periodic problems.
Invariant sets of solutions of Navier-Stokes and related evolution equations - A survey
Invariant wedges for a two-point reflecting Brownian motion and the “hot spots” problem.
Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
We construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost surely for data in a Fourier–Lebesgue space with and scaling like , for small . We also show the invariance of this measure.