Displaying similar documents to “Existence of solutions for Navier problems with degenerate nonlinear elliptic equations”

Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations Δ ( v ( x ) | Δ u | p - 2 Δ u ) - ∑ j = 1 n D j [ ω 1 ( x ) 𝒜 j ( x , u , ∇ u ) ] + b ( x , u , ∇ u ) ω 2 ( x ) = f 0 ( x ) - ∑ j = 1 n D j f j ( x ) , in Ω in the setting of the weighted Sobolev spaces.

Uniqueness of solutions for some degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro (2014)

Applicationes Mathematicae

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We investigate the existence and uniqueness of solutions to the Dirichlet problem for a degenerate nonlinear elliptic equation - ∑ i , j = 1 n D j ( a i j ( x ) D i u ( x ) ) + b ( x ) u ( x ) + d i v ( Φ ( u ( x ) ) ) = g ( x ) - ∑ j = 1 n f j ( x ) on Ω in the setting of the space H₀(Ω).

Solvability of the stationary Stokes system in spaces H ² - μ , μ ∈ (0,1)

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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We consider the stationary Stokes system with slip boundary conditions in a bounded domain. Assuming that data functions belong to weighted Sobolev spaces with weights equal to some power of the distance to some distinguished axis, we prove the existence of solutions to the problem in appropriate weighted Sobolev spaces.

Boundedness and stabilization in a three-dimensional two-species chemotaxis-Navier-Stokes system

Hirata, Misaki, Kurima, Shunsuke, Mizukami, Masaaki, Yokota, Tomomi

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This paper is concerned with the two-species chemotaxis-Navier–Stokes system with Lotka–Volterra competitive kinetics ( 1 ) t + u · 1 = 𝔻 1 - χ 1 · ( 1 c ) + μ 1 1 ( 1 - 1 - a 1 2 ) in × ( 0 , ∞ ) , ( 2 ) t + u · 2 = 𝔻 2 - χ 2 · ( 2 c ) + μ 2 2 ( 1 - a 2 1 - 2 ) in × ( 0 , ∞ ) , c t + u · c = 𝔻 c - ( α 1 + β 2 ) c in × ( 0 , ∞ ) , u t + ( u · ) u = 𝔻 u + ∇ P + ( γ 1 + 2 ) Φ , · u = 0 in × ( 0 , ∞ ) under homogeneous Neumann boundary conditions and initial conditions, where is a bounded domain in R3 with smooth boundary. Recently, in the 2-dimensional setting, global existence and stabilization of classical solutions to the above system were first established. However, the 3-dimensional case has not been studied: Because of difficulties in the Navier–Stokes system,...

Existence of solutions to the nonstationary Stokes system in H - μ 2 , 1 , μ ∈ (0,1), in a domain with a distinguished axis. Part 1. Existence near the axis in 2d

W. M. Zajączkowski (2007)

Applicationes Mathematicae

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We consider the nonstationary Stokes system with slip boundary conditions in a bounded domain which contains some distinguished axis. We assume that the data functions belong to weighted Sobolev spaces with the weight equal to some power function of the distance to the axis. The aim is to prove the existence of solutions in corresponding weighted Sobolev spaces. The proof is divided into three parts. In the first, the existence in 2d in weighted spaces near the axis is shown. In the...