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Uniqueness and regularity of weak solutions of a fluid-rigid body interaction system under the Prodi-Serrin condition Prodi-Serrin条件下流体-刚体相互作用系统弱解的唯一性和规律性
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023123
Debayan Maity, Takéo Takahashi
{"title":"Uniqueness and regularity of weak solutions of a fluid-rigid body interaction system under the Prodi-Serrin condition","authors":"Debayan Maity, Takéo Takahashi","doi":"10.3934/dcds.2023123","DOIUrl":"https://doi.org/10.3934/dcds.2023123","url":null,"abstract":"In this article, we study the weak uniqueness and the regularity of the weak solutions of a fluid-structure interaction system. More precisely, we consider the motion of a rigid ball in a viscous incompressible fluid and we assume that the fluid-rigid body system fills the entire space $ mathbb{R}^{3}. $ We prove that the corresponding weak solutions that additionally satisfy a classical Prodi-Serrin condition, including a critical one, are unique. We also show that the weak solutions are regular under the Prodi-Serrin conditions, with a smallness condition in the critical case.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135213132","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: 1
Stabilization in two-species chemotaxis systems with singular sensitivity and Lotka-Volterra competitive kinetics 具有奇异灵敏度和Lotka-Volterra竞争动力学的两种趋化系统的稳定性
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023130
Halil ibrahim Kurt, Wenxian Shen
{"title":"Stabilization in two-species chemotaxis systems with singular sensitivity and Lotka-Volterra competitive kinetics","authors":"Halil ibrahim Kurt, Wenxian Shen","doi":"10.3934/dcds.2023130","DOIUrl":"https://doi.org/10.3934/dcds.2023130","url":null,"abstract":"The current paper is concerned with the stabilization in the following parabolic-parabolic-elliptic chemotaxis system with singular sensitivity and Lotka-Volterra competitive kinetics, $ begin{equation} begin{cases} u_t = Delta u-chi_1 nablacdot (frac{u}{w} nabla w)+u(a_1-b_1u-c_1v) , quad &amp;xin Omegacr v_t = Delta v-chi_2 nablacdot (frac{v}{w} nabla w)+v(a_2-b_2v-c_2u), quad &amp;xin Omegacr 0 = Delta w-mu w +nu u+ lambda v, quad &amp;xin Omega cr frac{partial u}{partial n} = frac{partial v}{partial n} = frac{partial w}{partial n} = 0, quad &amp;xinpartialOmega, end{cases} end{equation}~~~~(1) $ where $ Omega subset mathbb{R}^N $ is a bounded smooth domain, and $ chi_i $, $ a_i $, $ b_i $, $ c_i $ ($ i = 1, 2 $) and $ mu, , nu, , lambda $ are positive constants. In [25], among others, we proved that for any given nonnegative initial data $ u_0, v_0in C^0(barOmega) $ with $ u_0+v_0not equiv 0 $, (1) has a unique globally defined classical solution $ (u(t, x;u_0, v_0), v(t, x;u_0, v_0), w(t, x;u_0, v_0)) $ with $ u(0, x;u_0, v_0) = u_0(x) $ and $ v(0, x;u_0, v_0) = v_0(x) $ in any space dimensional setting with any positive constants $ chi_i, a_i, b_i, c_i $ ($ i = 1, 2 $) and $ mu, nu, lambda $. In this paper, we assume that the competition in (1) is weak in the sense that $ frac{c_1}{b_2}<frac{a_1}{a_2}, quad frac{c_2}{b_1}<frac{a_2}{a_1}. $ Then (1) has a unique positive constant solution $ (u^*, v^*, w^*) $, where $ u^* = frac{a_1b_2-c_1a_2}{b_1b_2-c_1c_2}, quad v^* = frac{b_1a_2-a_1c_2}{b_1b_2-c_1c_2}, quad w^* = frac{nu}{mu}u^*+frac{lambda}{mu} v^*. $ We obtain some explicit conditions on $ chi_1, chi_2 $ which ensure that the positive constant solution $ (u^*, v^*, w^*) $ is globally stable, that is, for any given nonnegative initial data $ u_0, v_0in C^0(barOmega) $ with $ u_0not equiv 0 $ and $ v_0not equiv 0 $, $ limlimits_{ttoinfty}Big(|u(t, cdot;u_0, v_0)-u^*|_infty +|v(t, cdot;u_0, v_0)-v^*|_infty+|w(t, cdot;u_0, v_0)-w^*|_inftyBig) = 0. $","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135319721","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
Long time well-posedness of compressible magnetohydrodynamic boundary layer equations in Sobolev spaces Sobolev空间中可压缩磁流体边界层方程的长时间适定性
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023133
Shengxin Li, Feng Xie
{"title":"Long time well-posedness of compressible magnetohydrodynamic boundary layer equations in Sobolev spaces","authors":"Shengxin Li, Feng Xie","doi":"10.3934/dcds.2023133","DOIUrl":"https://doi.org/10.3934/dcds.2023133","url":null,"abstract":"In this paper we consider the long time well-posedness of solutions to two-dimensional compressible magnetohydrodynamic (MHD) boundary layer equations. When the initial data is a small perturbation of a steady solution with size of $ varepsilon $, then the lifespan of solutions in Sobolev spaces is proved to be greater than $ varepsilon^{-frac43} $. And such a result can be extended to the case that both initial data and far-field state are small perturbations around the steady states. Moreover, it holds true for both isentropic and non-isentropic magnetohydrodynamic boundary layer equations.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135560497","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
Multilinear Wiener-Wintner type ergodic averages and its application 多线性Wiener-Wintner型遍历平均及其应用
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023109
Rongzhong Xiao
{"title":"Multilinear Wiener-Wintner type ergodic averages and its application","authors":"Rongzhong Xiao","doi":"10.3934/dcds.2023109","DOIUrl":"https://doi.org/10.3934/dcds.2023109","url":null,"abstract":"This paper extends the generalized Wiener–Wintner Theorem built by Host and Kra to the multilinear case under the hypothesis of pointwise convergence of multilinear ergodic averages. In particular, we have the following result:Let $ (X, {mathcal B}, mu, T) $ be a measure preserving system. Let $ a $ and $ b $ be two distinct non-zero integers. Then for any $ f_{1}, f_{2}in L^{infty}(mu) $, there exists a full measure subset $ X(f_{1}, f_{2}) $ of $ X $ such that for any $ xin X(f_{1}, f_{2}) $, and any nilsequence $ {textbf b} = {b_n}_{nin {mathbb Z}} $,$ limlimits_{Nrightarrow infty}frac{1}{N}sumlimits_{n = 0}^{N-1}b_{n}f_{1}(T^{an}x)f_{2}(T^{bn}x) $exists.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135700495","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: 1
Anisotropic singular Trudinger-Moser inequalities on the whole Euclidean space 整个欧几里德空间上的各向异性奇异Trudinger-Moser不等式
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023111
Xiaomeng Li
{"title":"Anisotropic singular Trudinger-Moser inequalities on the whole Euclidean space","authors":"Xiaomeng Li","doi":"10.3934/dcds.2023111","DOIUrl":"https://doi.org/10.3934/dcds.2023111","url":null,"abstract":"Let $ F: mathbb{R}^nrightarrow [0, , infty) $ be a convex function of class $ C^2(mathbb{R}^nbackslash{0}) $, which is even and positively homogeneous of degree $ 1 $. In this paper, we prove that$ suplimits_{uin W^{1, n}(mathbb{R}^n), , displaystyle{int}_{mathbb{R}^n}(F^n(nabla u)+|u|^n)dxleq1}displaystyle{int}_{mathbb{R}^n}frac{Phi(lambda_{n}(1-frac{beta}{n})(1+alpha|u|^{n}_n)^{frac{1}{n-1}}|u|^{frac{n}{n-1}})}{F^o(x)^beta}dx $is finite for $ 0leqalpha<1 $, and the supremum is infinity for $ alphageq1 $, where $ F^o(x) $ is the polar function of $ F $, $ Phi(t) = e^t-sum_{j = 0}^{n-2}frac{t^j}{j!} $, $ betain[0, n) $, $ lambda_n = n^{frac{n}{n-1}}kappa_n^{frac{1}{n-1}} $ and $ kappa_n $ is the volume of the unit Wulff ball. Moreover, by using the method of blow-up analysis, we also obtain the existence of extremal functions for the supremum when $ 0leqalpha<1 $.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"2011 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136257651","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
Response solutions of a class of degenerate quasi-periodic systems with a small parameter 一类小参数退化拟周期系统的响应解
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023114
Xiaomei Yang, Junxiang Xu
{"title":"Response solutions of a class of degenerate quasi-periodic systems with a small parameter","authors":"Xiaomei Yang, Junxiang Xu","doi":"10.3934/dcds.2023114","DOIUrl":"https://doi.org/10.3934/dcds.2023114","url":null,"abstract":"This paper considers a special class of quasi-periodic systems with a small parameter, whose unperturbed part has a degenerate equilibrium point. We prove the existence of response solutions for many sufficiently small parameters. The proof is based on some formal KAM techniques and the Leray-Schauder Continuation Theorem.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306278","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 the scattering of subcritical defocusing generalized Korteweg-de Vries equation 亚临界散焦广义Korteweg-de Vries方程的散射
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023009
Taegyu Kim
{"title":"On the scattering of subcritical defocusing generalized Korteweg-de Vries equation","authors":"Taegyu Kim","doi":"10.3934/dcds.2023009","DOIUrl":"https://doi.org/10.3934/dcds.2023009","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"115 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85917227","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
Strong convergence in Bopp-Podolsky-Proca type constructions Bopp-Podolsky-Proca型结构的强收敛性
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023013
Emmanuel Hebey
{"title":"Strong convergence in Bopp-Podolsky-Proca type constructions","authors":"Emmanuel Hebey","doi":"10.3934/dcds.2023013","DOIUrl":"https://doi.org/10.3934/dcds.2023013","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88568088","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
Evolutionary bifurcation diagrams of A $ P $-Laplacian generalized logistic problem with nonnegative constant yield harvesting 非负恒产量收获的A $ P $- laplace广义logistic问题的进化分岔图
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023019
Kuo-Chih Hung, Shin-Hwa Wang, Jhih-Jyun Zeng
{"title":"Evolutionary bifurcation diagrams of A $ P $-Laplacian generalized logistic problem with nonnegative constant yield harvesting","authors":"Kuo-Chih Hung, Shin-Hwa Wang, Jhih-Jyun Zeng","doi":"10.3934/dcds.2023019","DOIUrl":"https://doi.org/10.3934/dcds.2023019","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"14 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73526469","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
Radially symmetric stationary solutions for certain chemotaxis systems in higher dimensions: A geometric approach 高维某些趋化系统的径向对称稳态解:一种几何方法
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2022188
Yutaka Ichida
{"title":"Radially symmetric stationary solutions for certain chemotaxis systems in higher dimensions: A geometric approach","authors":"Yutaka Ichida","doi":"10.3934/dcds.2022188","DOIUrl":"https://doi.org/10.3934/dcds.2022188","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"7 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75458327","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: 1
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