Weak solutions to a nonlinear variational wave equation with general data
Weak solutions to the Navier-Stokes equations in a Y-shaped domain
We prove the existence of weak solutions to the Navier-Stokes equations describing the motion of a fluid in a Y-shaped domain.
Weakly continuous operators. Applications to differential equations
The paper is a supplement to a survey by J. Franců: Monotone operators, A survey directed to differential equations, Aplikace Matematiky, 35(1990), 257–301. An abstract existence theorem for the equation with a coercive weakly continuous operator is proved. The application to boundary value problems for differential equations is illustrated on two examples. Although this generalization of monotone operator theory is not as general as the M-condition, it is sufficient for many technical applications....
Weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk.
Weakly nonlinear stability analysis of a thin magnetic fluid during spin coating.
Weakly stable multidimensional shocks
Weighted L² and approaches to fluid flow past a rotating body
Consider the flow of a viscous, incompressible fluid past a rotating obstacle with velocity at infinity parallel to the axis of rotation. After a coordinate transform in order to reduce the problem to a Navier-Stokes system on a fixed exterior domain and a subsequent linearization we are led to a modified Oseen system with two additional terms one of which is not subordinate to the Laplacean. In this paper we describe two different approaches to this problem in the whole space case. One of them...
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.
Well-posed solutions of the third order Benjamin-Ono equation in weighted Sobolev spaces.
Wellposedness and stability results for the Navier-Stokes equations in
Well-posedness for a class of non-Newtonian fluids with general growth conditions
The paper concerns uniqueness of weak solutions to non-Newtonian fluids with nonstandard growth conditions for the Cauchy stress tensor. We recall the results on existence of weak solutions and additionally provide the proof of existence of measure-valued solutions. Motivated by the fluids of strongly inhomogeneous behaviour and having the property of rapid shear thickening we observe that the described situation cannot be captured by power-law-type rheology. We describe the growth conditions with...
Well-posedness for density-dependent incompressible fluids with non-Lipschitz velocity
This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in with . We address the question of well-posedness for large and small initial data having critical Besov regularity in functional spaces as close as possible to the ones imposed in the incompressible Navier Stokes system by Cannone, Meyer and Planchon (where with ). This improves the classical analysis where is considered belonging in such that the velocity remains...
Well-posedness for systems representing electromagnetic/acoustic wavefront interaction
In this paper we consider dispersive electromagnetic systems in dielectric materials in the presence of acoustic wavefronts. A theory for existence, uniqueness, and continuous dependence on data is presented for a general class of systems which include acoustic pressure-dependent Debye polarization models for dielectric materials.
Well-posedness for Systems Representing Electromagnetic/Acoustic Wavefront Interaction
In this paper we consider dispersive electromagnetic systems in dielectric materials in the presence of acoustic wavefronts. A theory for existence, uniqueness, and continuous dependence on data is presented for a general class of systems which include acoustic pressure-dependent Debye polarization models for dielectric materials.
Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space , or . The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary...
Well-posedness issues for the Prandtl boundary layer equations
These notes are an introduction to the recent paper [7], about the well-posedness of the Prandtl equation. The difficulties and main ideas of the paper are described on a simpler linearized model.
Well-posedness of one-dimensional Korteweg models.
Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces Lsp(R2).
In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spacesLsp = (1 - ∆)-s/2 Lp(R2) with s > 1 + 2/p, 1 < p < ∞and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.
Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds