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On a Navier-Stokes type equation and inequality

Giovanni Prouse (1992)

Banach Center Publications

A Navier-Stokes type equation corresponding to a non-linear relationship between the stress tensor and the velocity deformation tensor is studied and existence and uniqueness theorems for the solution, in the 3-dimensional case, of the Cauchy-Dirichlet problem, for a bounded solution and for an almost periodic solution are given. An inequality which in some sense is the limit of the equation is also considered and existence theorems for the solution of the Cauchy-Dirichlet problems and for a periodic...

On the principal eigenvalue of elliptic operators in ℝ N and applications

Henry Berestycki, Luca Rossi (2006)

Journal of the European Mathematical Society

Two generalizations of the notion of principal eigenvalue for elliptic operators in ℝ N are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.

Oscillations of anharmonic Fourier series and the wave equation.

Alain Haraux, Vilmos Komornik (1985)

Revista Matemática Iberoamericana

In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of⎧     utt + (-1)m Δmu = 0     (t,x) ∈ R x Ω⎨⎩     u|Γ = ... = Δm-1 u|Γ = 0     t ∈ R.These results rely on the study of a sign of almost periodic functions of a special form restricted to a bounded interval J.

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