Related papers: The Dirichlet problem for the nonstationary Stokes…
In this paper, we study the solvability of a Cauchy- Dirichlet problem for nonlinear parabolic equation with non standard growths and nonlocal terms. We show the existence of weak solutions of the considered problem under more general…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
We study the Blackstock equation which models the propagation of nonlinear sound waves through dissipative fluids. Global well-posedness of the model with homogeneous Dirichlet boundary conditions is shown for small initial data. To this…
For many biological systems that involve elastic structures immersed in fluid, small length scales mean that inertial effects are also small, and the fluid obeys the Stokes equations. One way to solve the model equations representing such…
We are interested in the inverse problem of recovering a Robin coefficient defined on some non accessible part of the boundary from available data on another part of the boundary in the nonstationary Stokes system. We prove a Lipschitz…
We consider Stokes systems with measurable coefficients and Lions-type boundary conditions. We show that, in contrast to the Dirichlet boundary conditions, local boundary mixed-norm $L_{s,q}$-estimates hold for the spatial second-order…
The local existence of solutions to nonhomogeneous Navier-Stokes equations in cylindrical domains with arbitrary large flux is demonstrated. The existence is proved by the method of successive approximations. To show the existence with the…
In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a…
We introduce a general $L_p$-solvability result for the Poisson equation in non-smooth domains $\Omega\subset \mathbb{R}^d$, with the zero Dirichlet boundary condition. Our sole assumption on the domain $\Omega$ is the Hardy inequality:…
In this paper, we investigate existence of global-in-time strong solutions to the kinetic Cucker--Smale model coupled with the Stokes equations in the whole space. By introducing a weighted Sobolev space and using space-time estimates for…
We consider the Dirichlet problem on infinite and locally finite rooted trees, and we prove that the set of irregular points for continuous data has zero capacity. We also give some uniqueness results for solutions in Sobolev $ W^{1,p} $ of…
In this paper, we treat the corner singularity expansion and its convergence result regarding the penalized system obtained by eliminating the pressure variable in the Stokes problem of incompressible flow. The penalized problem is a kind…
We prove that the displacement problem of inhomogeneous elastostatics in a two--dimensional exterior Lipschitz domain has a unique solution with finite Dirichlet integral $\u$, vanishing uniformly at infinity if and only if the boundary…
We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…
This paper considers a class of noncoercive nonlinear elliptic problems with coefficients defined in Marcinkiewicz and Lorentz spaces. We prove the existence of a solution for the corresponding Dirichlet problem and investigate the higher…
The existence of suitable weak solutions of 3D Navier-Stokes equations, driven by a random body force, is proved. These solutions satisfy a local balance of energy. Moreover it is proved also the existence of a statistically stationary…
Consider the resolvent problem associated with the linearized viscous flow around a rotating body. Within a setting of classical Sobolev spaces, this problem is not well posed on the whole imaginary axis. Therefore, a framework of…
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…
Consider the unforced incompressible homogeneous Navier-Stokes equations on the $d$-torus $\mathbb{T}^d$ where $d\geq 4$ is the space dimension. It is shown that there exist nontrivial steady-state weak solutions $u\in L^{2}(\mathbb{T}^d)$.…