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Local well-posedness of solutions to 2D magnetic Prandtl model in the Prandtl-Hartmann regime

Yuming Qin, Xiuqing Wang, Junchen Liu (2025)

Applications of Mathematics

We consider the 2D magnetic Prandtl equation in the Prandtl-Hartmann regime in a periodic domain and prove the local existence and uniqueness of solutions by energy methods in a polynomial weighted Sobolev space. On the one hand, we have noted that the x -derivative of the pressure P plays a key role in all known results on the existence and uniqueness of solutions to the Prandtl-Hartmann regime equations, in which the case of favorable P ...

Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces

Gang Wu, Jia Yuan (2007)

Applicationes Mathematicae

We study local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation t u - ³ t x x u + 2 κ x u + x [ g ( u ) / 2 ] = γ ( 2 x u ² x x u + u ³ x x x u ) for the initial data u₀(x) in the Besov space B p , r s ( ) with max(3/2,1 + 1/p) < s ≤ m and (p,r) ∈ [1,∞]², where g:ℝ → ℝ is a given C m -function (m ≥ 4) with g(0)=g’(0)=0, and κ ≥ 0 and γ ∈ ℝ are fixed constants. Using estimates for the transport equation in the framework of Besov spaces, compactness arguments and Littlewood-Paley theory, we get a local well-posedness result.

Local-in-time existence for the non-resistive incompressible magneto-micropolar fluids

Peixin Zhang, Mingxuan Zhu (2022)

Applications of Mathematics

We establish the local-in-time existence of a solution to the non-resistive magneto-micropolar fluids with the initial data u 0 H s - 1 + ε , w 0 H s - 1 and b 0 H s for s > 3 2 and any 0 < ε < 1 . The initial regularity of the micro-rotational velocity w is weaker than velocity of the fluid u .

Localisation pour des opérateurs de Schrödinger aléatoires dans L 2 ( d ) : un modèle semi-classique

Frédéric Klopp (1995)

Annales de l'institut Fourier

Dans L 2 ( d ) , nous démontrons un résultat de localisation exponentielle pour un opérateur de Schrödinger semi-classique à potentiel périodique perturbé par de petites perturbations aléatoires indépendantes identiquement distribuées placées au fond de chaque puits. Pour ce faire, on montre que notre opérateur, restreint à un intervalle d’énergie convenable, est unitairement équivalent à une matrice aléatoire infinie dont on contrôle bien les coefficients. Puis, pour ce type de matrices, on prouve un résultat...

Localization effects for eigenfunctions near to the edge of a thin domain

Serguei A. Nazarov (2002)

Mathematica Bohemica

It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain Ω h is localized either at the whole lateral surface Γ h of the domain, or at a point of Γ h , while the eigenfunction decays exponentially inside Ω h . Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too.

Localizations of partial differential operators and surjectivity on real analytic functions

Michael Langenbruch (2000)

Studia Mathematica

Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set Ω n . Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization P m , Θ of the principal part P m is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for P m , Θ . Under additional assumptions P m must be locally hyperbolic.

Currently displaying 441 – 460 of 556