Search
Search Results
-
On the uniqueness of a suitable weak solution to the Navier–Stokes Cauchy problem
The paper is concerned with the Navier–Stokes Cauchy problem. We investigate on some results of regularity and uniqueness related to suitable weak...
-
Very Weak Solution of the Discrete Heat Equation with Irregular Time-Dependent Thermal Conductivity
In this paper, we investigate the semi-classical version of the heat equation with irregular time-dependent coefficients. When regular coefficients...
-
On Type I Blowups of Suitable Weak Solutions to the Navier–Stokes Equations Near Boundary
In this note, boundary Type I blowups of suitable weak solutions to the Navier–Stokes equations are discussed. In particular, it has been shown that,...
-
Existence of weak solution to initial-boundary value problem for finite order Kelvin–Voigt fluid motion model
The paper is devoted to the proof of a weak solution existence for the Kelvin–Voigt fluid motion model of an arbitrary finite order. First, for the...
-
Partial Regularity of Suitable Weak Solutions to the System of the Incompressible Shear-thinning Flow
This paper is devoted to the partial regularity of suitable weak solutions to the system of the incompressible shear-thinning flow in a bounded...
-
Existence of a Sign-Changing Weak Solution to Doubly Nonlinear Parabolic Equations
In this paper, assuming the initial-boundary datum belonging to suitable Sobolev and Lebesgue spaces, we prove the global existence result for a...
-
Asymptotics of the Solution to the Cauchy Problem for a Singularly Perturbed Operator Differential Transport Equation with Weak Diffusion
AbstractFormal asymptotic expansions of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation with...
-
Some New Properties of a Suitable Weak Solution to the Navier–Stokes Equations
The paper is concerned with the IBVP of the Navier–Stokes equations. The goal is the construction of a weak solution enjoying some new properties. Of...
-
Weak-strong uniqueness for three dimensional incompressible active liquid crystals
The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models. In this...
-
Weak Derivatives and Sobolev Spaces
The functional spaces defined in terms of classical derivatives are unfortunately not a suitable setting for a PDEs theory based on weak...
-
Weak and Weak* Topologies
In this chapter, we will study topologies on Banach spaces which are weaker (i.e., coarser) than the norm topology.
-
Weak solvability and well-posedness of some fractional parabolic problems with vanishing initial datum
This paper tackles a class of nonlinear parabolic equations driven by the fractional p -Laplacian operator with a vanishing initial datum. Our primary...
-
Nonuniqueness of Generalised Weak Solutions to the Primitive and Prandtl Equations
We develop a convex integration scheme for constructing nonunique weak solutions to the hydrostatic Euler equations (also known as the inviscid...
-
A unique weak solution for the fractional integro-differential schrödinger equations
In this study, by applying some nonlinear analysis results, it is demonstrated the existence of unique weak solution for a kind of nonlinear...
-
On weak (measure valued)–strong uniqueness for Navier–Stokes–Fourier system with Dirichlet boundary condition
In this article, our goal is to define a measure valued solution of compressible Navier–Stokes–Fourier system for a heat conducting fluid with...
-
Stochastic Navier–Stokes Variational Inequalities with Unilateral Boundary Conditions: Probabilistic Weak Solvability
We initiate the investigation of stochastic Navier–Stokes variational inequalities involving unilateral boundary conditions and nonlinear forcings...
-
Optimal partial regularity for very weak solutions to a class of nonlinear elliptic systems
We consider optimal partial regularity for very weak solutions to a class of nonlinear elliptic systems and obtain the general criterion for a very...