Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben

2005 | Buch

Stopping a Viscous Fluid by a Feedback Dissipative Field: Thermal Effects without Phase Changing Kapitel lesen Erstes Kapitel lesen

Trends in Partial Differential Equations of Mathematical Physics

herausgegeben von: José Francisco Rodrigues, Gregory Seregin, José Miguel Urbano

Verlag: Birkhäuser Basel

Buchreihe : Progress in Nonlinear Differential Equations and Their Applications

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Inhaltsverzeichnis

Frontmatter
Stopping a Viscous Fluid by a Feedback Dissipative Field: Thermal Effects without Phase Changing
Abstract
We show how the action on two simultaneous effects (a suitable coupling about velocity and temperature and a low range of temperature but upper that the phase changing one) may be responsible of stopping a viscous fluid without any changing phase. Our model involves a system, on an unbounded pipe, given by the planar stationary Navier-Stokes equation perturbed with a sublinear term f(x,θ, u) coupled with a stationary (and possibly nonlinear) advection diffusion equation for the temperature θ.
After proving some results on the existence and uniqueness of weak solutions we apply an energy method to show that the velocity u vanishes for x large enough.
S.N. Antontsev, J.I. Díaz, H.B. de Oliveira
Ultracontractive Bounds for Nonlinear Evolution Equations Governed by the Subcritical p-Laplacian
Abstract
We consider the equation https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_2/MediaObjects/978-3-7643-7317-7_2_IEq1_HTML.gif = Δp(u) with 2 ≤ p < d on a compact Riemannian manifold. We prove that any solution u(t) approaches its (time-independent) mean ū with the quantitative bound https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_2/MediaObjects/978-3-7643-7317-7_2_IEq2_HTML.gif for any q ∊ [2, +∞] and t > 0 and the exponents β, γ are shown to be the only possible for a bound of such type. The proof is based upon the connection between logarithmic Sobolev inequalities and decay properties of nonlinear semigroups.
Matteo Bonforte, Gabriele Grillo
Weighted L 2-spaces and Strong Solutions of the Navier-Stokes Equations in
Abstract
We consider the velocity field u(x, t) of a Navier-Stokes flow in the whole space.
We give a persistence result in a subspace of L 2( https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_3/MediaObjects/978-3-7643-7317-7_3_IEq2_HTML.gif , (1 + |x|2)5/2 dx), which allows us to fill the gap between previously known results in the weighted-L 2 setting and those on the pointwise decay of u at infinity.
Lorenzo Brandolese
A Limit Model for Unidirectional Non-Newtonian Flows with Nonlocal Viscosity
Abstract
A p-Laplacian flow (1 < p < ∞) with nonlocal diffusivity is obtained as an asymptotic limit case of a high thermal conductivity flow described by a coupled system involving the dissipation energy.
L. Consiglieri, J.F. Rodrigues, T. Shilkin
On the Problem of Thermocapillary Convection for Two Incompressible Fluids Separated by a Closed Interface
Abstract
We consider the unsteady motion of a drop in another incompressible fluid. On the unknown interface between the liquids, the surface tension is taken into account. Moreover, the coe cient of surface tension depends on the temperature. We study this problem of the thermocapillary convection by M.V. Lagunova and V.A. Solonnikov’s technique developed for a single liquid.
The local existence theorem for the problem is proved in Hölder classes of functions. The proof is based on the fact that the solvability of the problem with a constant coe cient of surface tension was obtain earlier. For a given velocity vector field of the fluids, we arrive at a di raction problem for the heat equation which solvability is established by well-known methods. Existence of a solution to the complete problem is proved by successive approximations.
Irina Vlad. Denisova
Some Mathematical Problems in Visual Transduction
Abstract
We present a mathematical model for the phototransduction cascade, taking into account the spatial localization of the different reaction processes. The geometric complexity of the problem (set in the rod outer segment) is simplified by a process of homogenization and concentration of capacity.
Daniele Andreucci, Paolo Bisegna, Emmanuele DiBenedetto
Global Regularity in Sobolev Spaces for Elliptic Problems with p-structure on Bounded Domains
Carsten Ebmeyer
Temperature Driven Mass Transport in Concentrated Saturated Solutions
Abstract
We study the phenomenon of thermally induced mass transport in partially saturated solutions under a thermal gradient, accompanied by deposition of the solid segregated phase on the “cold” boundary. We formulate a one-dimensional model including the displacement of all species (solvent, solute and segregated phase) and we analyze a typical case establishing existence and uniqueness.
Antonio Fasano, Mario Primicerio
Solvability of a Free Boundary Problem for the Navier-Stokes Equations Describing the Motion of Viscous Incompressible Nonhomogeneous Fluid
Abstract
We consider a time-dependent problem for a viscous incompressible nonhomogeneous fluid bounded by a free surface on which surface tension forces act. We prove the local in time solvability theorem for this problem in Sobolev function spaces. In the nonhomogeneous model the density of the fluid is unknown. Going over to Lagrange coordinates connected with the velocity vector field, we pass from the free boundary problem to the problem in the fixed boundary domain. Due to the continuity equation, in Lagrange coordinates the density is the same as at the initial moment of time. It gives us the possibility to apply the methods developed by V.A. Solonnikov for the case of incompressible fluid with constant density.
Elena Frolova
Duality Principles for Fully Nonlinear Elliptic Equations
Abstract
In this paper we use duality theory to associate certain measures to fully-nonlinear elliptic equations. These measures are the natural extension of the Mather measures to controlled stochastic processes and associated second-order elliptic equations. We apply these ideas to prove new a priori estimates for smooth solutions of fully nonlinear elliptic equations.
Diogo Aguiar Gomes
On the Bénard Problem
Abstract
In literature there is no mathematical proof of the experimentally trivial stability of the rest state for a layer of compressible fluid heated from above. In the case of layer heated from below it is known that the system shows a threshold in the temperature gradient below which the fluid is not sensible to the imposed difference of temperature. Only semi-empirical justifications are available for this phenomenon, see [6].
Neglecting the thermal conductivity, we are able to prove that for a layer of compressible fluid between two rigid planes kept at constant temperature, the rest state is linearly stable for every values of the parameters involved in two cases: a) the layer is heated from above; b) the layer is heated from below and the imposed gradient of temperature is less than a precise quantity, namely g/c p, where g is the gravity constant, and c p is the specific heat at constant pressure, known as adiabatic gradient.
Giovanna Guidoboni, Mariarosaria Padula
Exact Boundary Controllability for Quasilinear Wave Equations
Li Tatsien
Regularity of Euler Equations for a Class of Three-Dimensional Initial Data
Abstract
The 3D incompressible Euler equations with initial data characterized by uniformly large vorticity are investigated. We prove existence on long time intervals of regular solutions to the 3D incompressible Euler equations for a class of large initial data in bounded cylindrical domains. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to some 2D manifold. The approach is based on fast singular oscillating limits, nonlinear averaging and cancellation of oscillations in the nonlinear interactions for the vorticity field. With nonlinear averaging methods in the context of almost periodic functions, resonance conditions and a nonstandard small divisor problem, we obtain fully 3D limit resonant Euler equations. We establish the global regularity of the latter without any restriction on the size of 3D initial data and bootstrap this into the regularity on arbitrary large time intervals of the solutions of 3D Euler equations with weakly aligned uniformly large vorticity at t = 0.
A. Mahalov, B. Nicolaenko, C. Bardos, F. Golse
A Model of a Two-dimensional Pump
Piotr Bogusław Mucha
Regularity of a Weak Solution to the Navier-Stokes Equation in Dependence on Eigenvalues and Eigenvectors of the Rate of Deformation Tensor
Abstract
We formulate su cient conditions for regularity of a so-called suitable weak solution (v; p) in a sub-domain D of the time-space cylinder Q T by means of requirements on one of the eigenvalues or on the eigenvectors of the rate of deformation tensor.
Jiří Neustupa, Patrick Penel
Free Work and Control of Equilibrium Configurations
M. Padula
Stochastic Geometry Approach to the Kinematic Dynamo Equation of Magnetohydrodynamics
Abstract
We review the geometry of diffusion processes of differential forms on smooth compact manifolds, as a basis for the random representations of the kinematic dynamo equations on these manifolds. We realize these representations in terms of sequences of ordinary (for almost all times) differential equations. We construct the random symplectic geometry and the random Hamiltonian structure for these equations, and derive a new class of Poincaré-Cartan invariants of magnetohydrodynamics. We obtain a random Liouville invariant. We work out in detail the case of R 3.
Diego L. Rapoport
Quasi-Lipschitz Conditions in Euler Flows
Abstract
In mathematical models of incompressible flow problems, quasi-Lipschitz conditions present a useful link between a class of singular integrals and systems of ordinary differential equations. Such a condition, established in suitable form for the first-order derivatives of Newtonian potentials in https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_18/MediaObjects/978-3-7643-7317-7_18_IEq1_HTML.gif (Section 2) gives the main tool for the proof (in Sections 3–6) of the existence of a unique classical solution to Cauchy’s problem of Helmholtz’s vorticity transport equation with partial discretization in https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_18/MediaObjects/978-3-7643-7317-7_18_IEq2_HTML.gif for each bounded time interval. The solution depends continuously on its initial value and, in addition, fulfills a discretized form of Cauchy’s vorticity equation.
Reimund Rautmann
Interfaces in Solutions of Diffusion-absorption Equations in Arbitrary Space Dimension
Abstract
We study the Cauchy-Dirichlet problem for the degenerate parabolic equation
https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_19/MediaObjects/978-3-7643-7317-7_19_IEqu1_HTML.gif
with the parameters a ∊ https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_19/MediaObjects/978-3-7643-7317-7_19_IEq1_HTML.gif , m > 1, p > 0, satisfying the condition m + p ≥ 2. The problem domain ɛ is the exterior of the cylinder bounded by a simple-connected surface S, supp u 0 is an annular domain https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_19/MediaObjects/978-3-7643-7317-7_19_IEq2_HTML.gif . We show that the velocity of the outer interface Γ = ∂ {supp u(x, t)} is given by the formula https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_19/MediaObjects/978-3-7643-7317-7_19_IEq3_HTML.gif where II(x, t) is a solution of the degenerate elliptic equation
https://static-content.springer.com/image/chp%3A10.1007%2F3-7643-7317-2_19/MediaObjects/978-3-7643-7317-7_19_IEqu2_HTML.gif
,depending on t as a parameter. It is proved that the solution and its interface Γ preserve their initial regularity with respect to the space variables, and that they are real analytic functions of time t. We also show that the regularity of the velocity v is better than it was at the initial instant. For the space dimensions n = 1, 2, 3, these results were established in [8]. We propose a modification of the method of [8] that makes it applicable to equations with an arbitrary number of independent variables.
Sergei Shmarev
Estimates for Solutions of Fully Nonlinear Discrete Schemes
Abstract
We describe some estimates for solutions of nonlinear discrete schemes, which are analogues of fundamental estimates of Krylov and Safonov for linear elliptic partial differential equations and the resultant Schauder estimates for nonlinear elliptic equations of Evans, Krylov and Safonov.
Hung-Ju Kuo, Neil S. Trudinger
Metadaten
Titel
Trends in Partial Differential Equations of Mathematical Physics
herausgegeben von
José Francisco Rodrigues
Gregory Seregin
José Miguel Urbano
Copyright-Jahr
2005
Verlag
Birkhäuser Basel
Electronic ISBN
978-3-7643-7317-7
Print ISBN
978-3-7643-7165-4
DOI
https://doi.org/10.1007/b137135

Premium Partner

    Bildnachweise