Weak Solutions of an Initial Boundary Value Problem for an Incompressible Viscous Fluid with Nonnegative Density

Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

“…The proof of Lemma 2.3 is referred to [6] and we omit it here. The solution of (2.6) , (2.9) , C k = (C 1 , · · · , C m ), is the image of the element ϕ 0 ∈ K. We denote the corresponding operator by Λ: K → C(0, T ), Λϕ 0 = C k .…”

Strong solutions to the incompressible magnetohydrodynamic equations with vacuum

“…For H ≡ 0, the problem has been studied by many authors [8][9][10][11][12][13][14][15][16][17]. Very recently, Cho and Kim [18] showed that the problem has a unique local strong solution (ρ, u, p, θ ) with the main hypothesis inf ρ 0 = 0, in Ω (10) and some natural compatibility conditions: −div (2µ 0 du 0 ) + ∇p 0 = ρ…”

Analysis of an iterative method for variable density incompressible fluids

“…For simplicity of the presentation, we have normalized the viscosity to be one, and have considered no external forces. The existence of diverse notions of solutions for system (1.1 -1.5) has been much studied, as in Kazhikov [14], Ladyzhenskaya and Solonnikov [16], Padula [18], Kim [15], Antontzev et al [2], Simon [21], Salvi [20], Boldrini and Rojas-Medar [3,4] for instance. Here, we are interested in the iterative method used by Okamoto [17] to show existence and uniqueness of local and global solutions for problem (1.1-1.5).…”