Related papers: The Capillarity Problem for Compressible Liquids
We concern with the global existence and large time behavior of compressible fluids (including the inviscid gases, viscid gases, and Boltzmann gases) in an infinitely expanding ball. Such a problem is one of the interesting models in…
It is well known that in compact local Lipschitz neighborhood retracts in Euclidean space flat convergence for integer rectifiable currents amounts just to weak convergence. In the present paper we extend this result to integral currents in…
We consider the Rayleigh-Taylor problem for two compressible, immiscible, inviscid, barotropic fluids evolving with a free interface in the presence of a uniform gravitational field. After constructing Rayleigh-Taylor steady-state solutions…
In this paper, we introduce a Robin boundary analogue of the Orlicz-Minkowski problem, which seeks to find a capillary convex body with a prescribed capillary Orlicz surface area measure in the upper Euclidean half-space. We obtain the…
We study a singularly perturbed problem related to infinity Laplacian operator with prescribed boundary values in a region. We prove that solutions are locally (uniformly) Lipschitz continuous, they grow as a linear function, are strongly…
We study boundary value problems for bounded uniform domains in $\mathbb{R}^n$, $n\geq 2$, with non-Lipschitz (and possibly fractal) boundaries. We prove Poincar\'e inequalities with trace terms and uniform constants for uniform…
The study deals with the theory of interior capacities of condensers in a locally compact space, a condenser being treated here as a countable, locally finite collection of arbitrary sets with the sign +1 or -1 prescribed such that the…
We consider a Neumann problem for strictly convex variational functionals of linear growth. We establish the existence of minimisers among $\operatorname{W}^{1,1}$-functions provided that the domain under consideration is simply connected.…
We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…
A classical model for sources and sinks in a two-dimensional perfect incompressible fluid occupying a bounded domain dates back to Yudovich in 1966. In this model, on the one hand, the normal component of the fluid velocity is prescribed on…
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
The problem of capillary transport in fibrous porous materials at low levels of liquid saturation has been addressed. It has been demonstrated, that the process of liquid spreading in this type of porous materials at low saturation can be…
In this paper, we refine and complement McCann's results on binary-star systems \cite{McC06}, a compressible fluid model governed by the Euler-Poisson equations. We consider a general form of the equation of state that includes polytropic…
We study singular limit for scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach and Rossby numbers are proportional to a small parameter $\epsilon$. If the fluid is confined to an infinite slab,…
T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They…
The global regularity problem for the Boussinesq system is a well known open problem in mathematical fluid dynamics. As a follow up to our work \cite{EJSI}, we give examples of finite-energy and Lipschitz continuous velocity field and…
We consider vectorial problems in the calculus of variations with an additional pointwise constraint. Our admissible mappings ${\bf n}:\mathbb{R}^k\rightarrow \mathbb{R}^d$ satisfy ${\bf n}(x)\in M$, where $M$ is a manifold embedded in…
We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in…
In this paper, we prove a new type of energy estimates for the compressible Euler's equation with free boundary, with a boundary part and an interior part. These can be thought of as a generalization of the energies in Christodoulou and…