Results 51 to 60 of about 142 (127)

Exponential Growth and Properties of Solutions for a Forced System of Incompressible Navier–Stokes Equations in Sobolev–Gevrey Spaces

Mathematics
One problem of interest in the analysis of Navier–Stokes equations is concerned with the behavior of solutions for certain conditions in the forcing term or external force.
José Luis Díaz Palencia
doaj   +1 more source

Global Solvability of the Generalized Navier−Stokes System in Critical Besov Spaces

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper is devoted to the global solvability of the Navier−Stokes system with a fractional Laplacian (−Δ)α in Rn for n ≥ 2, where the convective term has the form (|u|m−1u)·∇u for m ≥ 1. By establishing the estimates for the difference u1m−1u1−u2m−1u2 in homogeneous Besov spaces and employing the maximal regularity property of (−Δ)α in Lorentz−Besov
Huiyang Zhang, Shiwei Cao, Qinghua Zhang, Dengfeng Lu   +3 more
wiley   +1 more source

Gevrey Regularity for A Fluid–Structure Interaction Model

Journal of Optimization Theory and Applications
A result of Gevrey regularity is ascertained for a semigroup which models a fluid-structure interaction problem. In this model, the fluid evolves in a piecewise smooth or convex geometry $\mathcal{O}$. On a portion of the boundary, a fourth order plate equation is coupled with the fluid through pressure and matching velocities. The key to obtaining the
George Avalos, Dylan McKnight, Sara McKnight   +2 more
openaire   +2 more sources

New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
In this paper, an algebraic decay rate for the radius of spatial analyticity of solutions to the Kawahara equation ∂tu+β∂x5u+α∂x3u+u∂xu=00,β≠ is investigated. With given analytic initial data having a fixed radius of analyticity σ0, we derive an algebraic decay rate σ(t) ~ |t|−1/2 for the uniform radius of spatial analyticity of solutions to the ...
Tegegne Getachew, Jaume Giné
wiley   +1 more source

On local Gevrey regularity for Gevrey vectors of subelliptic sums of squares: an elementary proof of a sharp Gevrey Kotake–Narasimhan theorem [PDF]

ANNALI DELL'UNIVERSITA' DI FERRARA, 2017
We study the regularity of Gevrey vectors for Hörmander operators $$ P = \sum_{j=1}^m X_j^2 + X_0 + c$$ where the $X_j$ are real vector fields and $c(x)$ is a smooth function, all in Gevrey class $G^{s}.$ The principal hypothesis is that $P$ satisfies the subelliptic estimate: for some $\varepsilon >0, \; \exists \,C$ such that $$\|v\|_\varepsilon^2
openaire   +2 more sources

Gevrey solvability and Gevrey regularity in differential complexes associated to locally integrable structures [PDF]

Transactions of the American Mathematical Society, 2011
The authors consider the differential complex associated to a locally integrable involutive structure. Assuming local solvability in the classical sense, they prove that also \(G^s\)-Gevrey solvability holds. The main tool in the proof is given by the theory of the ultradifferential operators of \textit{H. Komatsu} [J. Fac. Sci., Univ. Tokyo, Sect. I A
Caetano, Paulo A. S., Cordaro, Paulo D.
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Algebraic Lower Bounds on the Spatial Analyticity Radius for Higher Order Nonlinear Schrödinger Equations

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
We investigate the initial value problem associated to the higher order nonlinear Schrödinger equation i∂tu+−1j+1∂x2ju=u2ju x,t≠0∈ℝ,ux,0=u0x, where j ≥ 2 is any integer, u is a complex valued function, and the initial data u0 is real analytic on ℝ and has a uniform radius of spatial analyticity σ0 in the space variable.
Tegegne Getachew, Birilew Belayneh, Betre Shiferaw, Huaiqin Wu   +3 more
wiley   +1 more source

Decay Rate on the Radius of Spatial Analyticity to Solutions for the Modified Camassa–Holm Equation

Journal of Mathematics, Volume 2025, Issue 1, 2025.
The initial value problem associated with the modified Camassa–Holm equation for initial data u0(x) that is analytic on the line and having uniform radius of spatial analyticity σ0 is considered. We have shown the persistence of the radius of spatial analyticity till some time δ.
Tegegne Getachew, Yongqiang Fu
wiley   +1 more source

Gevrey regularity for integro-differential operators

Journal of Mathematical Analysis and Applications, 2015
We prove a regularity theory in the Gevrey class for a family of nonlocal differential equations of elliptic type.
Albanese, G, Fiscella, A, Valdinoci, E
openaire   +4 more sources