Well-posedness of mild solutions to the drift-diffusion and the vorticity equations in amalgam spaces
type: Item
instance of: scholarly article
title: Well-posedness of mild solutions to the drift-diffusion and the vorticity equations in amalgam spaces
zbMATH Open document ID: 1505.35339
author: Takeshi Suguro
published in: Journal of Mathematical Analysis and Applications
publication date: 2022-12-20T00:00:00Z
review text: The author studies parabolic equations with nonlocal quadratic nonlinearities such as the vorticity equation (related to the Navier-Stokes system) and equations for interacting particles (arising in chemotaxis, astrophysics and electrochemistry). In order to take into account possible solutions with a slow decay at infinity, the functional framework of the amalgam spaces is considered. In those spaces the behavior of the \(L^p\) Lebesgue norms is controlled over the whole in \(\mathbb{R}^n\) in the \(L^\nu\) sense. In particular, usual \(L^p\) and uniform local \(L^p\) spaces can be considered. The main results include local-in-time existence of solutions with the initial data in suitable amalgam spaces, global-in-time existence for small initial data, and some unconditional uniqueness results.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35D99
zbMATH DE Number: 7634990
zbMATH Keywords: drift-diffusion equations
zbMATH Keywords: chemotaxis
zbMATH Keywords: vorticity equation
zbMATH Keywords: mild solutions
zbMATH Keywords: amalgam spaces
zbMATH Keywords: local-in-time solvability
zbMATH Keywords: global solutions
MaRDI profile type: Publication
full work available at URL: j.jmaa.2022.126843
OpenAlex ID: W4308523110
cites work: Global solutions of two-dimensional Navier-Stokes and Euler equations
cites work: Unions et intersections d'espaces \(L^p\) invariantes par translation ou convolution
cites work: The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
cites work: Global regular and singular solutions for a model of gravitating particles
cites work: Local Energy Solutions to the Navier--Stokes Equations in Wiener Amalgam Spaces
cites work: A nonlinear heat equation with singular initial data
cites work: Product-Convolution Operators and Mixed-Norm Spaces
cites work: Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations
cites work: Global solutions of some chemotaxis and angiogenesis system in high space dimension
cites work: Stability of constant steady states of a chemotaxis model
cites work: Generalized Amalgams, With Applications to Fourier Transform
cites work: Amalgams of 𝐿^{𝑝} and 𝑙^{𝑞}
cites work: On the Navier-Stokes initial value problem. I
cites work: Navier-stokes flow in r3with measures as initial vorticity and morrey spaces
cites work: Two-dimensional Navier-Stokes flow with measures as initial vorticity
cites work: Q4461863
cites work: Harmonic Analysis on Amalgams of LP and lq
cites work: Global well-posedness for Keller-Segel system in Besov type spaces
cites work: Small solutions for nonlinear heat equations, the Navier-Stokes equation and the Keller-segel system in Besov and Triebel-Lizorkin spaces
cites work: Ill-posedness issue for the drift diffusion system in the homogeneous Besov spaces
cites work: On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
cites work: The Cauchy problem for quasi-linear symmetric hyperbolic systems
cites work: Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
cites work: Initiation of slime mold aggregation viewed as an instability
cites work: Calderón-Zygmund operators on amalgam spaces and in the discrete case
cites work: Well-posedness for the Navier-Stokes equations
cites work: Local existence and finite time blow-up of solutions in the 2-D Keller-Segel system
cites work: Existence and uniqueness theorem on weak solutions to the parabolic-elliptic Keller-Segel system
cites work: Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type.
cites work: Well-posedness for the drift-diffusion system in \(L^p\) arising from the semiconductor device simulation
cites work: Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller-Segel equations in the whole space
cites work: The Navier-Stokes equations with initial data in uniformly local \(L^p\) spaces.
cites work: Q4872331
cites work: Asymptotic Behavior for a Nonlinear Degenerate Diffusion Equation in Population Dynamics
cites work: The drift-diffusion system in two-dimensional critical Hardy space
cites work: Random walk with persistence and external bias
cites work: Well-posedness and unconditional uniqueness of mild solutions to the Keller-Segel system in uniformly local spaces
DOI: 10.1016/J.JMAA.2022.126843
description: scientific article; zbMATH DE number 7634990