A Variational Analysis of the Thermal Equilibrium State of Charged Quantum Fluids

Frank Pacard

doi:10.1080/03605309508821118

A Variational Analysis of the Thermal Equilibrium State of Charged Quantum Fluids

Frank Pacard

TU Berlin

Research output: Contribution to journal › Article › peer-review

Abstract

The thermal equilibrium state of a charged, isentropic quantum fluid in a bounded domain Ω is entirely described by the particle density n minimizing the total energy where ϕ = V[n_] + V^e solves Poisson’s equation - Δϕ = n - C subject to mixed Dirichlet-Neumann boundary conditions. It is shown that for given N > 0 (i. e. for prescribed total number of particles) this energy functional admits a unique minimizer in Furthermore it is proven that n ε C_loc¹(Ω) H L^∞(Ω) for all λ ε (0,1) and n > 0 in Ω.

Original language	English
Pages (from-to)	885-900
Number of pages	16
Journal	Communications in Partial Differential Equations
Volume	20
Issue number	5-6
DOIs	https://doi.org/10.1080/03605309508821118
Publication status	Published - 1 Jan 1995
Externally published	Yes

Keywords

thermal equilibrium state of quantum fluid quantum hydrodynamic model variational method for a semilinear elliptic system boundary value problem for nonlinear elliptic PDE a priori estimates smoothness and positivity of energy minimizer variational principles in thermodynamics

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10.1080/03605309508821118

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title = "A Variational Analysis of the Thermal Equilibrium State of Charged Quantum Fluids",

abstract = "The thermal equilibrium state of a charged, isentropic quantum fluid in a bounded domain Ω is entirely described by the particle density n minimizing the total energy where ϕ = V[n] + Ve solves Poisson{\textquoteright}s equation - Δϕ = n - C subject to mixed Dirichlet-Neumann boundary conditions. It is shown that for given N > 0 (i. e. for prescribed total number of particles) this energy functional admits a unique minimizer in Furthermore it is proven that n ε Cloc1(Ω) H L∞(Ω) for all λ ε (0,1) and n > 0 in Ω.",

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year = "1995",

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KW - thermal equilibrium state of quantum fluid quantum hydrodynamic model variational method for a semilinear elliptic system boundary value problem for nonlinear elliptic PDE a priori estimates smoothness and positivity of energy minimizer variational princi

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

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A Variational Analysis of the Thermal Equilibrium State of Charged Quantum Fluids

Abstract

Keywords

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