### Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity

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We consider the time-periodic Oseen flow around a rotating body in ℝ³. We prove a priori estimates in ${L}^{q}$-spaces of weak solutions for the whole space problem under the assumption that the right-hand side has the divergence form. After a time-dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional term -(ω ∧ x)·∇u + ω ∧ u in the equation of momentum where ω denotes the angular velocity. We prove the existence of generalized weak solutions in ${L}^{q}$-space...

Material and shape derivatives for solutions to the Dirichlet Laplacian in a half-space are derived by an application of the speed method. The proposed method is general and can be used for shape sensitivity analysis in unbounded domains for the Neumann Laplacian as well as for the elasticity boundary value problems.

The paper contains the proof of global existence of weak solutions of the viscous compressible barotropic gas for the initial-boundary value problem in a finite channel.

The paper contains the proof of global existence of weak solutions viscous compressible isothermal bipolar fluid of initial boundary value in a finite channel.

The global existence of weak solution is proved for the problem of the motion of several rigid bodies in a barotropic compressible fluid, under the influence of gravitational forces.

The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.

The paper describes the special situation of barotropic nonnewtonian fluid, where stress tensor can be written in the form of potentials which depend on ${e}_{ij}$ and $\left(\frac{\partial {e}_{ij}}{\partial {x}_{k}}\right)$. For this case, we prove the existence and uniqueness of weak solution.

We study a linear system of equations arising from fluid motion around a moving rigid body, where rotation is included. Originally, the coordinate system is attached to the fluid, which means that the domain is changing with respect to time. To get a problem in the fixed domain, the problem is rewritten in the coordinate system attached to the body. The aim of the present paper is the proof of the existence of a strong solution in a weighted Lebesgue space. In particular, we prove the existence...

We are interested in a barotropic motion of the non-Newtonian bipolar fluids . We consider a special case where the stress tensor is expressed in the form of potentials depending on and $\left(\frac{\partial {e}_{ij}}{\partial {x}_{k}}\right)$. We prove the asymptotic stability of the rest state under the assumption of the regularity of the potential forces.

We deal with the Laplace equation in the half space. The use of a special family of weigted Sobolev spaces as a framework is at the heart of our approach. A complete class of existence, uniqueness and regularity results is obtained for inhomogeneous Dirichlet problem.

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