Some notes to the transport equation and to the Green formula

Sébastien Novo; Antonín Novotný; Milan Pokorný

Displaying similar documents to “Some notes to the transport equation and to the Green formula”

Solvability of a first order system in three-dimensional non-smooth domains

Michal Křížek, Pekka Neittaanmäki (1985)

Aplikace matematiky

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A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain $Ω \subset 𝐑^{3}$ . On the boundary $δ Ω$ , the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.

On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation

Michal Křížek, Pekka Neittaanmäki (1989)

Aplikace matematiky

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The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.

On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion

Piotr Mucha, Wojciech Zajączkowski (2000)

Applicationes Mathematicae

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The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that $u \in W_{r}^{2, 1} ({\tilde{Ω}}^{T})$ with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the $L_{p}$ -approach the Lagrangian coordinates must be used....

Existence theorems for compressible viscous fluids having zero shear viscosity

Paolo Secchi (1984)

Rendiconti del Seminario Matematico della Università di Padova

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Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

Michal Křížek, Pekka Neittaanmäki (1984)

Aplikace matematiky

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The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given. ...

On the stationary motion of compressible viscous fluids

Paolo Secchi (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On a generalized Stokes problem

Václav Mácha (2011)

Open Mathematics

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We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space.