Nonlinearity最新文献

{"title":"Global higher regularity and decay estimates for positive solutions of fractional equations in RN *","authors":"Yinbin Deng, Xian Yang","doi":"10.1088/1361-6544/ad4503","DOIUrl":"https://doi.org/10.1088/1361-6544/ad4503","url":null,"abstract":"In the paper, we study the global higher regularity and decay estimates of the positive solutions for the following fractional equations <inline-formula>\u0000<tex-math><?CDATA $left{ begin{aligned} &left(-Deltaright)^s u+u = |u|^{p-2}uquad mathrm{in} mathbb{R}^N, &lim_{|x|toinfty}uleft(xright) = 0,quad uin H^sleft(mathbb{R}^Nright),quadquadquadquadtext{(0.1)} end{aligned} right. $?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mtable columnalign=\"left\" displaystyle=\"true\"><mml:mtr><mml:mtd><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign=\"left\" displaystyle=\"true\"><mml:mtr><mml:mtd></mml:mtd><mml:mtd><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mo>−</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>s</mml:mi></mml:msup><mml:mi>u</mml:mi><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>u</mml:mi><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mstyle scriptlevel=\"0\"></mml:mstyle><mml:mrow><mml:mi>in</mml:mi></mml:mrow><mml:mtext> </mml:mtext><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:msup><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd></mml:mtd><mml:mtd><mml:mi></mml:mi><mml:munder><mml:mo movablelimits=\"true\">lim</mml:mo><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>x</mml:mi><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mo accent=\"false\" stretchy=\"false\">→</mml:mo><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:mrow></mml:munder><mml:mi>u</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mstyle scriptlevel=\"0\"></mml:mstyle><mml:mi>u</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi>H</mml:mi><mml:mi>s</mml:mi></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable><mml:mo fence=\"true\" stretchy=\"true\" symmetric=\"true\"></mml:mo><mml:mspace width=\"12pt\"></mml:mspace><mml:mn>(0.1)</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"nonad4503eqn0_1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> where <inline-formula>\u0000<tex-math><?CDATA $sin(0,1)$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mi>s</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"nonad4503ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>, <inline-formula>\u0000<tex-math><?CDATA $Ngt2s$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mi>N</mml:mi><mml:mo>></mml:mo><mml:mn>2</mm","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"82 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939385","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":"Critical intermittency in rational maps","authors":"Ale Jan Homburg, Han Peters, Vahatra Rabodonandrianandraina","doi":"10.1088/1361-6544/ad42f9","DOIUrl":"https://doi.org/10.1088/1361-6544/ad42f9","url":null,"abstract":"Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in iterated function systems, and involves a superattracting periodic orbit. This paper will provide and study examples of iterated function systems by two rational maps on the Riemann sphere that give rise to critical intermittency. The main ingredient for this is a superattracting fixed point for one map that is mapped onto a common repelling fixed point by the other map. We include a study of topological properties such as topological transitivity.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"33 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939516","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":"Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment","authors":"Xiang Bai, Lin-An Li and Xiaojing Xu","doi":"10.1088/1361-6544/ad422b","DOIUrl":"https://doi.org/10.1088/1361-6544/ad422b","url":null,"abstract":"In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreover, we obtain this system has weak alignment behavior. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties caused by the nonlocal velocity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"22 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884716","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":"Absolutely continuous invariant measures for random dynamical systems of beta-transformations","authors":"Shintaro Suzuki","doi":"10.1088/1361-6544/ad3f68","DOIUrl":"https://doi.org/10.1088/1361-6544/ad3f68","url":null,"abstract":"We consider an independent and identically distributed (i.i.d.) random dynamical system of simple linear transformations on the unit interval (mod 1), , β > 0, which are the so-called beta-transformations. For such a random dynamical system, including the case that it is generated by uncountably many maps, we give an explicit formula for the density function of a unique stationary measure under the assumption that the random dynamics is expanding in mean. As an application, in the case that the random dynamics is generated by finitely many maps and the maps are chosen according to a Bernoulli measure, we show that the density function is analytic as a function of parameter in the Bernoulli measure and give its derivative explicitly. Furthermore, for a non-i.i.d. random dynamical system of beta-transformations, we also give an explicit formula for the random densities of a unique absolutely continuous invariant measure under a certain strong expanding condition or under the assumption that the maps randomly chosen are close to the beta-transformation for a non-simple number in the sense of parameter β.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"10 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838206","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":"On the Garden of Eden theorem for non-uniform cellular automata","authors":"Xuan Kien Phung","doi":"10.1088/1361-6544/ad3ffa","DOIUrl":"https://doi.org/10.1088/1361-6544/ad3ffa","url":null,"abstract":"We establish several extensions of the well-known Garden of Eden theorem for non-uniform cellular automata (CA) over the full shifts and over amenable group universes. In particular, our results describe quantitatively the relations between the partial pre-injectivity and the size of the image of a non-uniform CA. A strengthened surjunctivity result is also obtained for multi-dimensional CA over strongly irreducible subshifts of finite type.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"45 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140837998","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":"Global existence and blowup of solutions to a class of wave equations with Hartree type nonlinearity","authors":"Hongwei Zhang, Xiao Su and Shuo Liu","doi":"10.1088/1361-6544/ad3f67","DOIUrl":"https://doi.org/10.1088/1361-6544/ad3f67","url":null,"abstract":"In this paper, we consider a class of wave-Hartree equations on a bounded smooth convex domain with Dirichlet boundary condition. We prove the local existence of solutions in the natural energy space by using the standard Galërkin method. The results on global existence and nonexistence of solutions are obtained mainly by means of the potential well theory and concavity method.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"40 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811968","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":"Low Mach number limit on perforated domains for the evolutionary Navier–Stokes–Fourier system","authors":"Danica Basarić and Nilasis Chaudhuri","doi":"10.1088/1361-6544/ad3da9","DOIUrl":"https://doi.org/10.1088/1361-6544/ad3da9","url":null,"abstract":"We consider the Navier–Stokes–Fourier system describing the motion of a compressible, viscous and heat-conducting fluid on a domain perforated by tiny holes. First, we identify a class of dissipative solutions to the Oberbeck–Boussinesq approximation as a low Mach number limit of the primitive system. Secondly, by proving the weak–strong uniqueness principle, we obtain strong convergence to the target system on the lifespan of the strong solution.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"8 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806467","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":"A note on cascade flux laws for the stochastically-driven nonlinear Schrödinger equation","authors":"Jacob Bedrossian","doi":"10.1088/1361-6544/ad3794","DOIUrl":"https://doi.org/10.1088/1361-6544/ad3794","url":null,"abstract":"In this note we point out some simple sufficient (plausible) conditions for ‘turbulence’ cascades in suitable limits of damped, stochastically-driven nonlinear Schrödinger equation in a d-dimensional periodic box. Simple characterizations of dissipation anomalies for the wave action and kinetic energy in rough analogy with those that arise for fully developed turbulence in the 2D Navier–Stokes equations are given and sufficient conditions are given which differentiate between a ‘weak’ turbulence regime and a ‘strong’ turbulence regime. The proofs are relatively straightforward once the statements are identified, but we hope that it might be useful for thinking about mathematically precise formulations of the statistically-stationary wave turbulence problem.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"11 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803507","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":"Small-data global existence of solutions for the Pitaevskii model of superfluidity","authors":"Juhi Jang, Pranava Chaitanya Jayanti and Igor Kukavica","doi":"10.1088/1361-6544/ad3cae","DOIUrl":"https://doi.org/10.1088/1361-6544/ad3cae","url":null,"abstract":"We investigate a micro-scale model of superfluidity derived by Pitaevskii (1959 Sov. Phys. JETP8 282–7) to describe the interacting dynamics between the superfluid and normal fluid phases of Helium-4. The model involves the nonlinear Schrödinger equation (NLS) and the Navier–Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. Depending on the nature of the nonlinearity in the NLS, we prove global/almost global existence of solutions to this system in —strong in wavefunction and velocity, and weak in density.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"42 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803508","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":"Average shadowing revisited","authors":"Michael Blank","doi":"10.1088/1361-6544/ad3ac6","DOIUrl":"https://doi.org/10.1088/1361-6544/ad3ac6","url":null,"abstract":"We propose a novel unifying approach to study the shadowing property for a broad class of dynamical systems (in particular, discontinuous and non-invertible) under a variety of perturbations. In distinction to known constructions, our approach is local: it is based on the gluing property which takes into account the shadowing under a single (not necessarily small) perturbation.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"32 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140616404","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}