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Blow-up Analysis for the ({varvec{ab}})-Family of Equations $${{varvec{ab}}$ -方程组的炸毁分析
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-24 DOI: 10.1007/s00021-024-00857-4
Wenguang Cheng, Ji Lin
{"title":"Blow-up Analysis for the ({varvec{ab}})-Family of Equations","authors":"Wenguang Cheng,&nbsp;Ji Lin","doi":"10.1007/s00021-024-00857-4","DOIUrl":"10.1007/s00021-024-00857-4","url":null,"abstract":"<div><p>This paper investigates the Cauchy problem for the <i>ab</i>-family of equations with cubic nonlinearities, which contains the integrable modified Camassa–Holm equation (<span>(a = frac{1}{3})</span>, <span>(b = 2)</span>) and the Novikov equation (<span>(a = 0)</span>, <span>(b = 3)</span>) as two special cases. When <span>(3a + b ne 3)</span>, the <i>ab</i>-family of equations does not possess the <span>(H^1)</span>-norm conservation law. We give the local well-posedness results of this Cauchy problem in Besov spaces and Sobolev spaces. Furthermore, we provide a blow-up criterion, the precise blow-up scenario and a sufficient condition on the initial data for the blow-up of strong solutions to the <i>ab</i>-family of equations. Our blow-up analysis does not rely on the use of the conservation laws.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139945824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Linear Instability of Symmetric Logarithmic Spiral Vortex Sheets 对称对数螺旋涡旋片的线性不稳定性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-23 DOI: 10.1007/s00021-023-00847-y
Tomasz Cieślak, Piotr Kokocki, Wojciech S. Ożański
{"title":"Linear Instability of Symmetric Logarithmic Spiral Vortex Sheets","authors":"Tomasz Cieślak,&nbsp;Piotr Kokocki,&nbsp;Wojciech S. Ożański","doi":"10.1007/s00021-023-00847-y","DOIUrl":"10.1007/s00021-023-00847-y","url":null,"abstract":"<div><p>We consider Alexander spirals with <span>(Mge 3)</span> branches, that is symmetric logarithmic spiral vortex sheets. We show that such vortex sheets are linearly unstable in the <span>(L^infty )</span> (Kelvin–Helmholtz) sense, as solutions to the Birkhoff–Rott equation. To this end we consider Fourier modes in a logarithmic variable to identify unstable solutions with polynomial growth in time.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139945823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Temporal Regularity of Symmetric Stochastic p-Stokes Systems 对称随机 p-Stokes 系统的时间规律性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-21 DOI: 10.1007/s00021-024-00852-9
Jörn Wichmann
{"title":"Temporal Regularity of Symmetric Stochastic p-Stokes Systems","authors":"Jörn Wichmann","doi":"10.1007/s00021-024-00852-9","DOIUrl":"10.1007/s00021-024-00852-9","url":null,"abstract":"<div><p>We study the symmetric stochastic <i>p</i>-Stokes system, <span>(p in (1,infty ))</span>, in a bounded domain. The results are two-fold: First, we show that in the context of analytically weak solutions, the stochastic pressure—related to non-divergence free stochastic forces—enjoys almost <span>(-1/2)</span> temporal derivatives on a Besov scale. Second, we verify that the velocity <i>u</i> of strong solutions obeys 1/2 temporal derivatives in an exponential Nikolskii space. Moreover, we prove that the non-linear symmetric gradient <span>(V(mathbb {epsilon } u) = (kappa + left| mathbb {epsilon } uright| )^{(p-2)/2} mathbb {epsilon } u)</span>, <span>(kappa ge 0)</span>, which measures the ellipticity of the <i>p</i>-Stokes system, has 1/2 temporal derivatives in a Nikolskii space.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00852-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Weak Solutions to the Multicomponent Reactive Flows Driven by Non-conservative Boundary Conditions 论非保守边界条件驱动的多组分反应流的弱解
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-20 DOI: 10.1007/s00021-024-00856-5
Bingkang Huang
{"title":"On the Weak Solutions to the Multicomponent Reactive Flows Driven by Non-conservative Boundary Conditions","authors":"Bingkang Huang","doi":"10.1007/s00021-024-00856-5","DOIUrl":"10.1007/s00021-024-00856-5","url":null,"abstract":"<div><p>We propose a new concept of weak solutions to the multicomponent reactive flows driven by large boundary data. When the Gibbs’ equation incorporates the species mass fractions, we establish the global-in-time existence of weak solutions for any finite energy initial data. Moreover, if the classical solutions exist, the weak solutions coincide with them in the same time interval.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction 流体-硬球相互作用随时间变化的运动稳定性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-19 DOI: 10.1007/s00021-024-00854-7
Toshiaki Hishida
{"title":"Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction","authors":"Toshiaki Hishida","doi":"10.1007/s00021-024-00854-7","DOIUrl":"10.1007/s00021-024-00854-7","url":null,"abstract":"<div><p>We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the incompressible Navier–Stokes system, whereas the motion of the body is governed by the balance for linear and angular momentum. Both motions are affected by each other at the boundary. Assuming that the rigid body is a ball, we adopt a monolithic approach to deduce <span>(L^q)</span>–<span>(L^r)</span> decay estimates of solutions to a non-autonomous linearized system. We then apply those estimates to the full nonlinear initial value problem to find temporal decay properties of the disturbance. Although the shape of the body is not allowed to be arbitrary, the present contribution is the first attempt at analysis of the large time behavior of solutions around nontrivial basic states, that can be time-dependent, for the fluid–structure interaction problem and provides us with a stability theorem which is indeed new even for steady motions under the self-propelling condition or with wake structure.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00854-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global Solutions of 3D Isentropic Compressible Navier–Stokes Equations with Two Slow Variables 具有两个慢变量的三维等熵可压缩纳维-斯托克斯方程的全局解决方案
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-19 DOI: 10.1007/s00021-024-00855-6
NanNan Yang
{"title":"Global Solutions of 3D Isentropic Compressible Navier–Stokes Equations with Two Slow Variables","authors":"NanNan Yang","doi":"10.1007/s00021-024-00855-6","DOIUrl":"10.1007/s00021-024-00855-6","url":null,"abstract":"<div><p>Motivated by Lu and Zhang (J Differ Equ 376:406–468, 2023), we prove the global existence of solutions to the three-dimensional isentropic compressible Navier–Stokes equations with smooth initial data slowly varying in two directions. In such a setting, the <span>(L^2)</span>-norms of the initial data are of order <span>(O(varepsilon ^{-1}))</span>, which are large.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139911269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Stokes System Arising in a Free Surface Viscous Flow of a Horizontally Periodic Fluid with Fractional Boundary Operators 关于水平周期流体自由表面粘性流动中出现的斯托克斯系统与分数边界算子
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-12 DOI: 10.1007/s00021-023-00850-3
Daisuke Hirata
{"title":"On a Stokes System Arising in a Free Surface Viscous Flow of a Horizontally Periodic Fluid with Fractional Boundary Operators","authors":"Daisuke Hirata","doi":"10.1007/s00021-023-00850-3","DOIUrl":"10.1007/s00021-023-00850-3","url":null,"abstract":"<div><p>In this note we investigate the initial-boundary value problem for a Stokes system arising in a free surface viscous flow of a horizontally periodic fluid with fractional boundary operators. We derive an integral representation of solutions by making use of the multiple Fourier series. Moreover, we demonstrate a unique solvability in the framework of the Sobolev space of <span>(L^2)</span>-type.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139750824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
2D Voigt Boussinesq Equations 二维 Voigt 布森斯方程
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-02 DOI: 10.1007/s00021-023-00849-w
Mihaela Ignatova
{"title":"2D Voigt Boussinesq Equations","authors":"Mihaela Ignatova","doi":"10.1007/s00021-023-00849-w","DOIUrl":"10.1007/s00021-023-00849-w","url":null,"abstract":"<div><p>We consider a critical conservative Voigt regularization of the 2D incompressible Boussinesq system on the torus. We prove the existence and uniqueness of global smooth solutions and their convergence in the smooth regime to the Boussinesq solution when the regularizations are removed. We also consider a range of mixed (subcritical–supercritical) Voigt regularizations for which we prove the existence of global smooth solutions.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139670224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Initial-Boundary Value Problems for One-Dimensional pth Power Viscous Reactive Gas with Density-Dependent Viscosity 密度随粘度变化的一维 pth 动力粘性反应气体的初始边界值问题
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-01-29 DOI: 10.1007/s00021-023-00846-z
Yongkai Liao
{"title":"Initial-Boundary Value Problems for One-Dimensional pth Power Viscous Reactive Gas with Density-Dependent Viscosity","authors":"Yongkai Liao","doi":"10.1007/s00021-023-00846-z","DOIUrl":"10.1007/s00021-023-00846-z","url":null,"abstract":"<div><p>Although there are many results on the global solvability and the precise description of the large time behaviors of solutions to the initial-boundary value/Cauchy problem of the one-dimensional pth power viscous reactive gas with positive constant viscosity, no result is available up to now for the corresponding problems with density-dependent viscosity. The main purpose of this paper is to study the global existence and asymptotic behavior of solutions to three types of initial-boundary value problems of 1d pth power viscous reactive gas with density-dependent viscosity and large initial data. The key ingredient in our analysis is to deduce the positive lower and upper bounds on both the specific volume and the absolute temperature.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139644661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Almost Sure Well-Posedness for Hall MHD 霍尔 MHD 的近乎确定的良好假设性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-01-29 DOI: 10.1007/s00021-023-00848-x
Mimi Dai
{"title":"Almost Sure Well-Posedness for Hall MHD","authors":"Mimi Dai","doi":"10.1007/s00021-023-00848-x","DOIUrl":"10.1007/s00021-023-00848-x","url":null,"abstract":"<div><p>We consider the magnetohydrodynamics system with Hall effect accompanied with initial data in supercritical Sobolev space. Via an appropriate randomization of the supercritical initial data, both local and small data global well-posedness for the system are obtained almost surely in critical Sobolev space.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139644826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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