Results 51 to 60 of about 518 (155)

Gevrey regularity for the supercritical quasi-geostrophic equation

, 2014
In this paper, following the techniques of Foias and Temam, we establish suitable Gevrey class regularity of solutions to the supercritical quasi-geostrophic equations in the whole space, with initial data in “critical” Sobolev spaces.
Biswas, Animikh
core   +1 more source

Well-Posedness in M-Ultradifferentiable Spaces for Weakly Hyperbolic Cauchy Problems with Hölder Continuous Coefficients

ITEGAM-JETIA
In this article, we demonstrate the weakly hyperbolic Cauchy problem under Hölder's regularity of a coefficient depending on time in the context of M-ultradifferentiable well-posedness.
Said Bouaziz, Khaled Benmeriem, Laid Gasmi   +2 more
doaj   +1 more source

On the well-posedness of weakly hyperbolic equations with time-dependent coefficients [PDF]

, 2012
30.10.12 KB.
Garetto, Claudia, Garetto, C, Claudia Garetto, Claudia Garetto (1253247), Ruzhansky, M, Michael Ruzhansky (7160006), Ruzhansky, Michael, Michael Ruzhansky   +7 more
core   +1 more source

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

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

Minimal Microlocal Gevrey Regularity for "Sums of Squares"

, 2009
A theorem of minimal microlocal Gevrey regularity is proved for operators that are sums of squares of vector fields with real analytic coefficients, thus providing a microlocal version of a well-known theorem of Derridj and Zuily("Regularite analytique ...
Bove, A, ALBANO, PAOLO, Albano, P, BOVE, ANTONIO, Chinni, G, CHINNI, GREGORIO   +5 more
core   +1 more source

Gevrey regularity for the Vlasov-Poisson system

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2021
We prove propagation of \frac{1}{s} -Gevrey regularity (s \in (0,1]) for the Vlasov-Poisson system on \mathbb{T}^{d} \times \mathbb{R}^{d} using a Fourier space method in analogy ...
openaire   +3 more sources

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