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Communications in Partial Differential Equations最新文献

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On the motion of a small rigid body in a viscous compressible fluid 关于小刚体在粘性可压缩流体中的运动
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-08-16 DOI: 10.1080/03605302.2023.2202733
E. Feireisl, Arnab Roy, A. Zarnescu
{"title":"On the motion of a small rigid body in a viscous compressible fluid","authors":"E. Feireisl, Arnab Roy, A. Zarnescu","doi":"10.1080/03605302.2023.2202733","DOIUrl":"https://doi.org/10.1080/03605302.2023.2202733","url":null,"abstract":"Abstract We consider the motion of a small rigid object immersed in a viscous compressible fluid in the 3-dimensional Eucleidean space. Assuming the object is a ball of a small radius ε we show that the behavior of the fluid is not influenced by the object in the asymptotic limit The result holds for the isentropic pressure law for any under mild assumptions concerning the rigid body density. In particular, the latter may be bounded as soon as The proof uses a new method of construction of the test functions in the weak formulation of the problem, and, in particular, a new form of the so-called Bogovskii operator.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44618489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 7
Gradient estimates for the Schrödinger potentials: convergence to the Brenier map and quantitative stability Schrödinger势的梯度估计:收敛到Brenier映射和定量稳定性
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-07-28 DOI: 10.1080/03605302.2023.2215527
Alberto Chiarini, Giovanni Conforti, Giacomo Greco, Luca Tamanini
{"title":"Gradient estimates for the Schrödinger potentials: convergence to the Brenier map and quantitative stability","authors":"Alberto Chiarini, Giovanni Conforti, Giacomo Greco, Luca Tamanini","doi":"10.1080/03605302.2023.2215527","DOIUrl":"https://doi.org/10.1080/03605302.2023.2215527","url":null,"abstract":"Abstract We show convergence of the gradients of the Schrödinger potentials to the (uniquely determined) gradient of Kantorovich potentials in the small-time limit under general assumptions on the marginals, which allow for unbounded densities and supports. Furthermore, we provide novel quantitative stability estimates for the optimal values and optimal couplings for the Schrödinger problem (SP), that we express in terms of a negative order weighted homogeneous Sobolev norm. The latter encodes the linearized behavior of the 2-Wasserstein distance between the marginals. The proofs of both results highlight for the first time the relevance of gradient bounds for Schrödinger potentials, that we establish here in full generality, in the analysis of the short-time behavior of Schrödinger bridges. Finally, we discuss how our results translate into the framework of quadratic Entropic Optimal Transport, that is a version of SP more suitable for applications in machine learning and data science.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42942787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 7
Scaling asymptotics of Wigner distributions of harmonic oscillator orbital coherent states 谐振子轨道相干态Wigner分布的标度渐近性
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-07-04 DOI: 10.1080/03605302.2023.2180754
Nicholas Lohr
{"title":"Scaling asymptotics of Wigner distributions of harmonic oscillator orbital coherent states","authors":"Nicholas Lohr","doi":"10.1080/03605302.2023.2180754","DOIUrl":"https://doi.org/10.1080/03605302.2023.2180754","url":null,"abstract":"Abstract The main result of this article gives scaling asymptotics of the Wigner distributions of isotropic harmonic oscillator orbital coherent states concentrating along Hamiltonian orbits γ in shrinking tubes around γ in phase space. In particular, these Wigner distributions exhibit a hybrid semi-classical scaling. That is, simultaneously, we have an Airy scaling when the tube has radius normal to the energy surface Σ E , and a Gaussian scaling when the tube has radius tangent to Σ E .","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47897552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 2
On the blow-up analysis at collapsing poles for solutions of singular Liouville-type equations 奇异Liouville型方程解的崩溃极点爆破分析
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-06-30 DOI: 10.1080/03605302.2022.2139725
G. Tarantello
{"title":"On the blow-up analysis at collapsing poles for solutions of singular Liouville-type equations","authors":"G. Tarantello","doi":"10.1080/03605302.2022.2139725","DOIUrl":"https://doi.org/10.1080/03605302.2022.2139725","url":null,"abstract":"Abstract We analyze a blow-up sequence of solutions for Liouville-type equations involving Dirac measures with “collapsing” poles. We consider the case where blow-up occurs exactly at a point where the poles coalesce. After proving that a” quantization” property still holds for the” blow-up mass,” we obtain precise pointwise estimates when blow-up occurs with the least blow-up mass. Interestingly, such estimates express the exact analogue of those previously obtained for solutions of “regular” Liouville equations where the “collapsing” Dirac measures are neglected. Such information will be used in a forthcoming paper to describe the asymptotic behavior of minimizers of the Donaldson functional introduced by Goncalves and Uhlenbeck in 2007, yielding to mean curvature 1-immersions of surfaces into hyperbolic 3-manifolds.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42857832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation 一维聚焦三次非线性薛定谔方程吉布斯测度的微观推导
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-06-07 DOI: 10.1080/03605302.2023.2243491
Andrew Rout, Vedran Sohinger
{"title":"A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation","authors":"Andrew Rout, Vedran Sohinger","doi":"10.1080/03605302.2023.2243491","DOIUrl":"https://doi.org/10.1080/03605302.2023.2243491","url":null,"abstract":"Abstract In this paper, we give a microscopic derivation of Gibbs measures for the focusing cubic nonlinear Schrödinger equation on the one-dimensional torus from many-body quantum Gibbs states. Since we are not making any positivity assumptions on the interaction, it is necessary to introduce a truncation of the mass in the classical setting and of the rescaled particle number in the quantum setting. Our methods are based on a perturbative expansion of the interaction, similarly as in [1]. Due to the presence of the truncation, the obtained series have infinite radius of convergence. We treat the case of bounded, L 1 and delta function interaction potentials, without any sign assumptions. Within this framework, we also study time-dependent correlation functions. This is the first such known result in the focusing regime.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45121507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 5
A Hamilton-Jacobi approach to evolution of dispersal 扩散演化的Hamilton-Jacobi方法
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-05-11 DOI: 10.1080/03605302.2022.2139723
King-Yeung Lam, Y. Lou, B. Perthame
{"title":"A Hamilton-Jacobi approach to evolution of dispersal","authors":"King-Yeung Lam, Y. Lou, B. Perthame","doi":"10.1080/03605302.2022.2139723","DOIUrl":"https://doi.org/10.1080/03605302.2022.2139723","url":null,"abstract":"Abstract The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait, with the trait acting directly on the dispersal (diffusion) rate, was formulated by Perthame and Souganidis [Math. Model. Nat. Phenom. 11:154–166, 2016] to study the evolution of random dispersal toward the evolutionarily stable strategy. For the rare mutation limit, it was shown that the equilibrium population concentrates on a single trait associated to the smallest dispersal rate. In this paper, we consider the corresponding evolution equation and characterize the asymptotic behaviors of the time-dependent solutions in the rare mutation limit, under mild convexity assumptions on the underlying Hamiltonian function.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43656126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case 周期哈密顿量紧支持扰动的消失折扣逼近:一维情况
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-05-10 DOI: 10.1080/03605302.2023.2183409
I. Capuzzo Dolcetta, A. Davini
{"title":"On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case","authors":"I. Capuzzo Dolcetta, A. Davini","doi":"10.1080/03605302.2023.2183409","DOIUrl":"https://doi.org/10.1080/03605302.2023.2183409","url":null,"abstract":"Abstract We study the asymptotic behavior of the viscosity solutions of the Hamilton-Jacobi (HJ) equation as the positive discount factor λ tends to 0, where is the perturbation of a Hamiltonian –periodic in the space variable and convex and coercive in the momentum, by a compactly supported potential The constant c(G) appearing above is defined as the infimum of values for which the HJ equation in admits bounded viscosity subsolutions. We prove that the functions locally uniformly converge, for to a specific solution of the critical equation We identify in terms of projected Mather measures for G and of the limit to the unperturbed periodic problem. Our work also includes a qualitative analysis of the critical equation with a weak KAM theoretic flavor.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48236363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 3
Phenotypic heterogeneity in a model of tumour growth: existence of solutions and incompressible limit 肿瘤生长模型的表型异质性:存在解决方案和不可压缩极限
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-04-12 DOI: 10.1080/03605302.2023.2191265
N. David
{"title":"Phenotypic heterogeneity in a model of tumour growth: existence of solutions and incompressible limit","authors":"N. David","doi":"10.1080/03605302.2023.2191265","DOIUrl":"https://doi.org/10.1080/03605302.2023.2191265","url":null,"abstract":"Abstract We consider a (degenerate) cross-diffusion model of tumour growth structured by phenotypic trait. We prove the existence of weak solutions and the incompressible limit as the pressure becomes stiff extending methods recently introduced in the context of two-species cross-diffusion systems. In the stiff-pressure limit, the compressible model generates a free boundary problem of Hele-Shaw type. Moreover, we prove a new L 4-bound on the pressure gradient.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43923487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 4
Fractional Sobolev regularity for fully nonlinear elliptic equations 完全非线性椭圆型方程的分数阶Sobolev正则性
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-04-06 DOI: 10.1080/03605302.2022.2059676
Edgard A. Pimentel, Makson S. Santos, E. Teixeira
{"title":"Fractional Sobolev regularity for fully nonlinear elliptic equations","authors":"Edgard A. Pimentel, Makson S. Santos, E. Teixeira","doi":"10.1080/03605302.2022.2059676","DOIUrl":"https://doi.org/10.1080/03605302.2022.2059676","url":null,"abstract":"Abstract We prove higher-order fractional Sobolev regularity for fully nonlinear, uniformly elliptic equations in the presence of unbounded source terms. More precisely, we show the existence of a universal number depending only on ellipticity constants and dimension, such that if u is a viscosity solution of then, with appropriate estimates. Our strategy suggests a sort of fractional feature of fully nonlinear diffusion processes, as what we actually show is that for a universal constant We believe our techniques are flexible and can be adapted to various models and contexts.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43226099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 2
Shock interactions for the Burgers-Hilbert equation 汉堡-希尔伯特方程的激波相互作用
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-04-05 DOI: 10.1080/03605302.2022.2084628
A. Bressan, S. Galtung, Katrin Grunert, K. Nguyen
{"title":"Shock interactions for the Burgers-Hilbert equation","authors":"A. Bressan, S. Galtung, Katrin Grunert, K. Nguyen","doi":"10.1080/03605302.2022.2084628","DOIUrl":"https://doi.org/10.1080/03605302.2022.2084628","url":null,"abstract":"Abstract This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with H 2 regularity away from the shocks plus a corrector term having an asymptotic behavior like close to each shock. A key step in the analysis is the construction of piecewise smooth solutions with a single shock for a general class of initial data.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48607242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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