Advances in Nonlinear Analysis最新文献

{"title":"Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs","authors":"Daniele Cassani, Lele Du","doi":"10.1515/anona-2023-0103","DOIUrl":"https://doi.org/10.1515/anona-2023-0103","url":null,"abstract":"Abstract We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <m:msubsup> <m:mrow> <m:mi>W</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> <m:mrow> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi mathvariant=\"normal\">Ω</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mspace width=\"0.33em\" /> <m:mo>↪</m:mo> <m:mspace width=\"0.33em\" /> <m:msup> <m:mrow> <m:mi>L</m:mi> </m:mrow> <m:mrow> <m:mi>q</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi mathvariant=\"normal\">Ω</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:math> {W}_{0}^{s,p}(Omega )hspace{0.33em}hookrightarrow hspace{0.33em}{L}^{q}(Omega ), where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>N</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:math> Nge 1 , <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mn>0</m:mn> <m:mo><</m:mo> <m:mi>s</m:mi> <m:mo><</m:mo> <m:mn>1</m:mn> </m:math> 0lt slt 1 , <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> </m:math> p=1,2 , <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mn>1</m:mn> <m:mo>≤</m:mo> <m:mi>q</m:mi> <m:mo><</m:mo> <m:msubsup> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mi>s</m:mi> </m:mrow> <m:mrow> <m:mo>∗</m:mo> </m:mrow> </m:msubsup> <m:mo>=</m:mo> <m:mfrac> <m:mrow> <m:mi>N</m:mi> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> <m:mo>−</m:mo> <m:mi>s</m:mi> <m:mi>p</m:mi> </m:mrow> </m:mfrac> </m:math> 1le qlt {p}_{s}^{ast }=frac{Np}{N-sp} , and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo>⊂</m:mo> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> </m:math> Omega subset {{mathbb{R}}}^{N} is a bounded smooth domain or the whole space <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> </m:math> {{mathbb{R}}}^{N} . Our results cover the borderline case <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:math> p=1 , the Hilbert case <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:math> p=2 , <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>N</m:mi> <m:mo>></m:mo> <m:mn>2</m:mn> <m:mi>s</m:mi> </m:math> Ngt 2s , and the so-called Sobolev limiting case <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>N</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:math> N=1 , <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>s</m:mi> <m:mo>=</m:mo> <m:mfrac> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:mfrac>","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135910104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability of stationary solutions to the three-dimensional Navier-Stokes equations with surface tension","authors":"Keiichi Watanabe","doi":"10.1515/anona-2022-0279","DOIUrl":"https://doi.org/10.1515/anona-2022-0279","url":null,"abstract":"Abstract This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. More precisely, this article considers the stability of equilibrium figure of uniformly rotating viscous incompressible fluid in R 3 {{mathbb{R}}}^{3} , which are rotationally symmetric about a certain axis. It is proved that this stability result can be obtained by the positivity of the second variation of the energy functional associated with the equation that determines an equilibrium figure, provided that initial data are close to an equilibrium state. The unique global solution is constructed in the L p {L}^{p} -in-time and L q {L}^{q} -in-space setting with ( p , q ) ∈ ( 2 , ∞ ) × ( 3 , ∞ ) left(p,q)in left(2,infty )times left(3,infty ) satisfying 2 / p + 3 / q < 1 2hspace{0.1em}text{/}p+3text{/}hspace{0.1em}qlt 1 , where the solution becomes real analytic, jointly in time and space. It is also proved that the solution converges exponentially to the equilibrium.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44851901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterizations for the genuine Calderón-Zygmund operators and commutators on generalized Orlicz-Morrey spaces","authors":"V. Guliyev, Meriban N. Omarova, M. Ragusa","doi":"10.1515/anona-2022-0307","DOIUrl":"https://doi.org/10.1515/anona-2022-0307","url":null,"abstract":"Abstract In this article, we show continuity of commutators of Calderón-Zygmund operators [ b , T ] left[b,T] with BMO functions in generalized Orlicz-Morrey spaces M Φ , φ ( R n ) {M}^{Phi ,varphi }left({{mathbb{R}}}^{n}) . We give necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators T T and for their commutators [ b , T ] left[b,T] on generalized Orlicz-Morrey spaces, respectively.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44624523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Incompressible limit for compressible viscoelastic flows with large velocity","authors":"Xianpeng Hu, Yaobin Ou, Dehua Wang, Lu Yang","doi":"10.1515/anona-2022-0324","DOIUrl":"https://doi.org/10.1515/anona-2022-0324","url":null,"abstract":"Abstract We are concerned with the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the three-dimensional compressible viscoelastic equations. The incompressibility is achieved by the large value of the volume viscosity, which is different from the low Mach number limit. To obtain the uniform estimates, we establish the estimates for the potential part and the divergence-free part of the velocity. As the volume viscosity goes to infinity, the dispersion associated with the pressure waves tends to disappear, but the large volume viscosity provides a strong dissipation on the potential part of the velocity forcing the flow to be almost incompressible.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42191352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and nonexistence of nontrivial solutions for the Schrödinger-Poisson system with zero mass potential","authors":"Xiaoping Wang, Fulai Chen, Fangfang Liao","doi":"10.1515/anona-2022-0319","DOIUrl":"https://doi.org/10.1515/anona-2022-0319","url":null,"abstract":"Abstract In this article, under some weaker assumptions on a > 0 agt 0 and f f , the authors aim to study the existence of nontrivial radial solutions and nonexistence of nontrivial solutions for the following Schrödinger-Poisson system with zero mass potential − Δ u + ϕ u = − a ∣ u ∣ p − 2 u + f ( u ) , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-a{| u| }^{p-2}u+fleft(u),& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. where p ∈ 2 , 12 5 pin left(2,frac{12}{5}right) . In particular, as a corollary for the following system: − Δ u + ϕ u = − ∣ u ∣ p − 2 u + ∣ u ∣ q − 2 u , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , left{begin{array}{ll}-Delta u+phi u=-{| u| }^{p-2}u+{| u| }^{q-2}u,& xin {{mathbb{R}}}^{3}, -Delta phi ={u}^{2},& xin {{mathbb{R}}}^{3},end{array}right. a sufficient and necessary condition is obtained on the existence of nontrivial radial solutions.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46259460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Short-time existence of a quasi-stationary fluid–structure interaction problem for plaque growth","authors":"Helmut Abels, Yadong Liu","doi":"10.1515/anona-2023-0101","DOIUrl":"https://doi.org/10.1515/anona-2023-0101","url":null,"abstract":"Abstract We address a quasi-stationary fluid–structure interaction problem coupled with cell reactions and growth, which comes from the plaque formation during the stage of the atherosclerotic lesion in human arteries. The blood is modeled by the incompressible Navier-Stokes equation, while the motion of vessels is captured by a quasi-stationary equation of nonlinear elasticity. The growth happens when both cells in fluid and solid react, diffuse and transport across the interface, resulting in the accumulation of foam cells, which are exactly seen as the plaques. Via a fixed-point argument, we derive the local well-posedness of the nonlinear system, which is sustained by the analysis of decoupled linear systems.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetry and nonsymmetry of minimal action sign-changing solutions for the Choquard system","authors":"Jianqing Chen, Qian Zhang","doi":"10.1515/anona-2022-0286","DOIUrl":"https://doi.org/10.1515/anona-2022-0286","url":null,"abstract":"Abstract In this article, we consider the following Choquard system in R N N ≥ 1 {{mathbb{R}}}^{N}Nge 1 − Δ u + u = 2 p p + q ( I α ∗ ∣ v ∣ q ) ∣ u ∣ p − 2 u , − Δ v + v = 2 q p + q ( I α ∗ ∣ u ∣ p ) ∣ v ∣ q − 2 v , u ( x ) → 0 , v ( x ) → 0 as ∣ x ∣ → ∞ , left{begin{array}{l}-Delta u+u=frac{2p}{p+q}({I}_{alpha }ast | v{| }^{q})| u{| }^{p-2}u, -Delta v+v=frac{2q}{p+q}({I}_{alpha }ast | u{| }^{p})| v{| }^{q-2}v, uleft(x)to 0,vleft(x)to 0hspace{1em}hspace{0.1em}text{as}hspace{0.1em}hspace{0.33em}| x| to infty ,end{array}right. where N + α N < p , q < N + α N − 2 frac{N+alpha }{N}lt p,qlt frac{N+alpha }{N-2} , 2 ∗ α {2}_{ast }^{alpha } denotes N + α N − 2 frac{N+alpha }{N-2} if N ≥ 3 Nge 3 and 2 ∗ α ≔ ∞ {2}_{ast }^{alpha }:= infty if N = 1 , 2 N=1,2 , I α {I}_{alpha } is a Riesz potential. By analyzing the asymptotic behavior of Riesz potential energy, we prove that minimal action sign-changing solutions have an odd symmetry with respect to the a hyperplane when α alpha is either close to 0 or close to N N . Our results can be regarded as a generalization of the results by Ruiz et al.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44885067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blow-up for compressible Euler system with space-dependent damping in 1-D","authors":"Jinbo Geng, Ning-An Lai, Manwai Yuen, Jiang Zhou","doi":"10.1515/anona-2022-0304","DOIUrl":"https://doi.org/10.1515/anona-2022-0304","url":null,"abstract":"Abstract This article considers the Cauchy problem for compressible Euler system in R {bf{R}} with damping, in which the coefficient depends on the space variable. Assuming the initial density has a small perturbation around a constant state and both the small perturbation and the small initial velocity field are compact supported, finite-time blow-up result will be established. This result reveals the fact that if the space-dependent damping coefficient decays fast enough in the far field (belongs to L 1 ( R ) {L}^{1}left({bf{R}}) ), then the damping is non-effective to the long-time behavior of the solution.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42971196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiplicity results for fractional Schrödinger-Kirchhoff systems involving critical nonlinearities","authors":"Soraya Fareh, K. Akrout, A. Ghanmi, Dušan D. Repovš","doi":"10.1515/anona-2022-0318","DOIUrl":"https://doi.org/10.1515/anona-2022-0318","url":null,"abstract":"Abstract In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional p p -Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we establish the multiplicity of solutions for such systems.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42239069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the topological gradient method for an inverse problem resolution","authors":"Mohamed Abdelwahed, Nejmeddine Chorfi","doi":"10.1515/anona-2023-0109","DOIUrl":"https://doi.org/10.1515/anona-2023-0109","url":null,"abstract":"Abstract In this work, we consider the topological gradient method to deal with an inverse problem associated with three-dimensional Stokes equations. The problem consists in detecting unknown point forces acting on fluid from measurements on the boundary of the domain. We present an asymptotic expansion of the considered cost function using the topological sensitivity analysis method. A detection algorithm is then presented using the developed formula. Some numerical tests are presented to show the efficiency of the presented algorithm.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136304599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}