{"title":"Stability of planar rarefaction waves in the vanishing dissipation limit of the Navier–Stokes–Fourier system","authors":"Eduard Feireisl , Wladimir Neves","doi":"10.1016/j.jfa.2025.110840","DOIUrl":"10.1016/j.jfa.2025.110840","url":null,"abstract":"<div><div>We consider the vanishing dissipation limit of the compressible Navier–Stokes–Fourier system, where the initial data approach a profile generating a planar rarefaction wave for the limit Euler system. We show that the associated weak solutions converge unconditionally to the planar rarefaction wave strongly in the energy norm.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 8","pages":"Article 110840"},"PeriodicalIF":1.7,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172494","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}
Filippo Riva , Giovanni Scilla , Francesco Solombrino
{"title":"Inertial Balanced Viscosity (IBV) solutions to infinite-dimensional rate-independent systems","authors":"Filippo Riva , Giovanni Scilla , Francesco Solombrino","doi":"10.1016/j.jfa.2025.110830","DOIUrl":"10.1016/j.jfa.2025.110830","url":null,"abstract":"<div><div>A suitable notion of weak solution to infinite-dimensional rate-independent systems, called Inertial Balanced Viscosity (IBV) solution, is introduced. The key feature of such notion is that the energy dissipated at jump discontinuities takes both into account inertial and viscous effects. Under a general set of assumptions it is shown that IBV solutions arise as vanishing inertia and viscosity limits of second order dynamic evolutions as well as of the corresponding time-incremental approximations. Relevant examples coming from applications, such as Allen-Cahn type evolutions and Kelvin-Voigt models in linearized elasticity, are considered.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110830"},"PeriodicalIF":1.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132572","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}
{"title":"Extremal problems in BMO and VMO involving the Garsia norm","authors":"Konstantin M. Dyakonov","doi":"10.1016/j.jfa.2025.110833","DOIUrl":"10.1016/j.jfa.2025.110833","url":null,"abstract":"<div><div>Given an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> function <em>f</em> on the unit circle <span><math><mi>T</mi></math></span>, we put<span><span><span><math><msub><mrow><mi>Φ</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>P</mi><mo>(</mo><mo>|</mo><mi>f</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>(</mo><mi>z</mi><mo>)</mo><mo>−</mo><mo>|</mo><mi>P</mi><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace><mi>z</mi><mo>∈</mo><mi>D</mi><mo>,</mo></math></span></span></span> where <span><math><mi>D</mi></math></span> is the open unit disk and <span><math><mi>P</mi></math></span> is the Poisson integral operator. The Garsia norm <span><math><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>G</mi></mrow></msub></math></span> is then defined as <span><math><msub><mrow><mi>sup</mi></mrow><mrow><mi>z</mi><mo>∈</mo><mi>D</mi></mrow></msub><mo></mo><msub><mrow><mi>Φ</mi></mrow><mrow><mi>f</mi></mrow></msub><msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span>, and the space BMO is formed by the functions <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> with <span><math><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>G</mi></mrow></msub><mo><</mo><mo>∞</mo></math></span>. If <span><math><msubsup><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><msub><mrow><mi>Φ</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>(</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span> for some point <span><math><msub><mrow><mi>z</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mi>D</mi></math></span>, then <em>f</em> is said to be a norm-attaining BMO function, written as <span><math><mi>f</mi><mo>∈</mo><msub><mrow><mi>BMO</mi></mrow><mrow><mi>na</mi></mrow></msub></math></span>. Note that <span><math><msub><mrow><mi>BMO</mi></mrow><mrow><mi>na</mi></mrow></msub></math></span> contains VMO, the space of functions with vanishing mean oscillation. We study, first, the functions <em>f</em> in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> (as well as in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>∩</mo><msub><mrow><mi>BMO</mi></mrow><mrow><mi>na</mi></mrow></msub></math></span>) with the property that <span><math><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>G</mi></mrow></msub><mo>=</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mo>∞</mo></mrow></msub></math></span>. The analytic case, where <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> gets replaced by <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></m","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110833"},"PeriodicalIF":1.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132578","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}
{"title":"Scattering for Schrödinger operators with conical decay","authors":"Adam Black , Tal Malinovitch","doi":"10.1016/j.jfa.2025.110831","DOIUrl":"10.1016/j.jfa.2025.110831","url":null,"abstract":"<div><div>We study the scattering properties of Schrödinger operators with potentials that have short-range decay along a collection of rays in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. This generalizes the classical setting of short-range scattering in which the potential is assumed to decay along <em>all</em> rays. For these operators, we give a microlocal characterization of the scattering states in terms of the dynamics and a corresponding description of their complement. This shows that any state decomposes into an asymptotically free piece and a piece that may interact with the potential for long times. We also show that, in certain cases, these characterizations can be purely spatial.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110831"},"PeriodicalIF":1.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Krzysztof Bogdan , Michał Gutowski , Katarzyna Pietruska-Pałuba
{"title":"Polarized Hardy–Stein identity","authors":"Krzysztof Bogdan , Michał Gutowski , Katarzyna Pietruska-Pałuba","doi":"10.1016/j.jfa.2025.110827","DOIUrl":"10.1016/j.jfa.2025.110827","url":null,"abstract":"<div><div>We prove the Hardy–Stein identity for vector functions in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>;</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> with <span><math><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mo>∞</mo></math></span> and for the canonical paring of two real functions in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> with <span><math><mn>2</mn><mo>≤</mo><mi>p</mi><mo><</mo><mo>∞</mo></math></span>. To this end we propose a notion of Bregman co-divergence and study the corresponding integral forms.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110827"},"PeriodicalIF":1.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132580","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}
{"title":"K-closedness results in noncommutative Lebesgue spaces with filtrations","authors":"Hugues Moyart","doi":"10.1016/j.jfa.2025.110829","DOIUrl":"10.1016/j.jfa.2025.110829","url":null,"abstract":"<div><div>In this paper, we establish a new general <em>K</em>-closedness result in the context of real interpolation of noncommutative Lebesgue spaces involving filtrations. As an application, we derive <em>K</em>-closedness results for various classes of noncommutative martingale Hardy spaces, addressing a problem raised by Randrianantoanina. The proof of this general result adapts Bourgain's approach to the real interpolation of classical Hardy spaces on the disk within the framework of noncommutative martingales.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110829"},"PeriodicalIF":1.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132576","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}
{"title":"Monotone rearrangement does not increase generalized Campanato norm in VMO","authors":"Leonid Slavin , Pavel Zatitskii","doi":"10.1016/j.jfa.2025.110828","DOIUrl":"10.1016/j.jfa.2025.110828","url":null,"abstract":"<div><div>We consider a quantitative version of the space VMO on an interval, equipped with a quadratic Campanato-type norm, and prove that monotone rearrangement does not increase the norm in this space.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110828"},"PeriodicalIF":1.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reducibility for the linearized two-component intermediate long-wave equation","authors":"Ying Fu , Changzheng Qu , Xiaoping Wu","doi":"10.1016/j.jfa.2025.110832","DOIUrl":"10.1016/j.jfa.2025.110832","url":null,"abstract":"<div><div>In this paper, we study the reducibility of a class of linear operators depending on time quasi-periodically, which arises from linearizing the two-component intermediate long-wave equation at a small amplitude quasi-periodic function, with a Diophantine frequency vector <span><math><mi>ω</mi><mo>∈</mo><msub><mrow><mi>O</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>ν</mi></mrow></msup></math></span>. We prove that there exists a Cantor-like set <span><math><msub><mrow><mi>O</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>⊂</mo><msub><mrow><mi>O</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> such that for every <span><math><mi>ω</mi><mo>∈</mo><msub><mrow><mi>O</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>, these operators can be reduced to the ones with constant coefficients by some linear, real, reversibility-preserving and quasi-periodic time-dependent transformations. As a conclusion, the stability of the solutions of the linearized two-component intermediate long-wave equation is obtained. Besides the KAM reducibility transformation, these transformations are obtained from some pseudo-differential operators and the flows of some PDEs. The key difficulty lies in estimating the norms and the upper and lower bounds of the operators related to the integral operator <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>δ</mi></mrow></msub></math></span> due to their complicated structures. To overcome the difficulties, we treat these operators as the principal pseudo-differential operators up to the remainders of lower order and impose some constraints on the parameters.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110832"},"PeriodicalIF":1.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132611","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}
{"title":"Non-existence and multiplicity of positive solutions for Choquard equations with critical combined nonlinearities","authors":"Shiwang Ma","doi":"10.1016/j.jfa.2025.110826","DOIUrl":"10.1016/j.jfa.2025.110826","url":null,"abstract":"<div><div>We study the non-existence and multiplicity of positive solutions of the nonlinear Choquard type equation<span><span><span>(<em>P</em><sub><em>ε</em></sub>)</span><span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>ε</mi><mi>u</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>⁎</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mrow><mi>in</mi></mrow><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span> is an integer, <span><math><mi>p</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mi>α</mi></mrow><mrow><mi>N</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mi>α</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>]</mo></math></span>, <span><math><mi>q</mi><mo>∈</mo><mo>(</mo><mn>2</mn><mo>,</mo><mfrac><mrow><mn>2</mn><mi>N</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>]</mo></math></span>, <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> is the Riesz potential of order <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>N</mi><mo>)</mo></math></span> and <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> is a parameter. We fix one of <span><math><mi>p</mi><mo>,</mo><mi>q</mi></math></span> as a critical exponent (in the sense of Hardy-Littlewood-Sobolev and Sobolev inequalities) and view the others in <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>ε</mi><mo>,</mo><mi>α</mi></math></span> as parameters, we find regions in the <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>ε</mi><mo>)</mo></math></span>-parameter space, such that the corresponding equation has no positive ground state or admits multiple positive solutions. This is a counterpart of the Brezis-Nirenberg Conjecture (Brezis and Nirenberg, 1983 <span><span>[7]</span></span>) for nonlocal elliptic equation in the whole space. Particularly, some threshold results for the existence of ground states and some conditions which insure two positive solutions are obtained. These results are quite different in nature from the corresponding local equation with combined powers nonlinearity and reveal the special influence of the nonlocal term. To the best of our knowledge, the only two papers concerning the multiplicity of positive solutions of elliptic equations with critical growth nonlinearity are given by Atkinson and Peletier (1986) <span><span>[5]</span></span> for elliptic equation on a ball and Wei and Wu (2023) <span><span>[40]</span></span> for elliptic equati","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110826"},"PeriodicalIF":1.7,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132574","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}
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