Results 1 to 10 of about 74 (69)
Boundedness of Littlewood-Paley Operators Associated with Gauss Measures
Journal of Inequalities and Applications, 2010 Modeled on the Gauss measure, the authors introduce the locally doubling measure metric space (𝒳,d,μ)ρ, which means that the set 𝒳 is endowed with a metric d and a locally doubling regular Borel measure μ ...
Liguang Liu, Dachun Yang
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On the stabilizing effect of rotation in the 3d Euler equations
Communications on Pure and Applied Mathematics, Volume 76, Issue 12, Page 3553-3641, December 2023., 2023 Abstract While it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More precisely, we investigate stability in the 3d rotating Euler equations in R3$\mathbb {R}^3$ with a fixed speed of rotation.
Yan Guo +3 more
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Communications on Pure and Applied Mathematics, Volume 76, Issue 12, Page 3685-3768, December 2023., 2023 Abstract We investigate the long‐time properties of the two‐dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ε. Under the classical Miles‐Howard stability condition on the Richardson number, we prove that the system experiences a shear‐buoyancy instability: the density variation
Jacob Bedrossian +3 more
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Energy Science &Engineering, Volume 11, Issue 7, Page 2444-2468, July 2023., 2023 Mode representation of power energy utilization processes and coupling integration effects of swarm intelligence (sparrow) methods. Abstract With the development of the electric market, electric load forecasting has been increasingly pursued by many scholars.
Guo‐Feng Fan +4 more
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Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 In this paper, we work on the Cauchy problem of the three‐dimensional micropolar fluid equations. For small initial data, in the variable‐exponent Fourier–Besov spaces, we achieve the global well‐posedness result. The Littlewood–Paley decomposition method and the Fourier‐localization technique are main tools to obtain the results. Moreover, the results
Muhammad Zainul Abidin +4 more
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Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023 Let L = −Δ + V be a Schrödinger operator on ℝn, where Δ denotes the Laplace operator ∑i=1n∂2/∂xi2 and V is a nonnegative potential belonging to a certain reverse Hölder class RHq(ℝn) with q > n/2. In this paper, by the regularity estimate of the fractional heat kernel related with L, we establish the quantitative weighted boundedness of Littlewood ...
Li Yang, Pengtao Li, Andrea Scapellato
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AxiomsLet L=−Δ+V be a Schrödinger operator, where Δ is the Laplacian defined on Rn and the nonnegative potential V satisfies the reverse Hölder inequality.
Chunmei Zhang +2 more
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A priori bounds for the generalised parabolic Anderson model
Communications on Pure and Applied Mathematics, Volume 79, Issue 5, Page 1315-1394, May 2026.Abstract We show a priori bounds for solutions to (∂t−Δ)u=σ(u)ξ$(\partial _t - \Delta) u = \sigma (u) \xi$ in finite volume in the framework of Hairer's Regularity Structures [Invent Math 198:269–504, 2014]. We assume σ∈Cb2(R)$\sigma \in C_b^2 (\mathbb {R})$ and that ξ$\xi$ is of negative Hölder regularity of order −1−κ$- 1 - \kappa$ where κ<κ¯$\kappa <
Ajay Chandra +2 more
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Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
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