Annals of Pde最新文献_第10页

Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle 有限长喷管内二维定常可压缩Euler流的跨声速接触间断稳定性

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-09-23 DOI: 10.1007/s40818-021-00113-2

Feimin Huang, Jie Kuang, Dehua Wang, Wei Xiang

{"title":"Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle","authors":"Feimin Huang, Jie Kuang, Dehua Wang, Wei Xiang","doi":"10.1007/s40818-021-00113-2","DOIUrl":"10.1007/s40818-021-00113-2","url":null,"abstract":"<div><p>We consider the stability of transonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle. This is the first work on the mixed-type problem of transonic flows across a contact discontinuity as a free boundary in nozzles. We start with the Euler-Lagrangian transformation to straighten the contact discontinuity in the new coordinates. However, the upper nozzle wall in the subsonic region depending on the mass flux becomes a free boundary after the transformation. Then we develop new ideas and techniques to solve the free-boundary problem in three steps: (1) we fix the free boundary and generate a new iteration scheme to solve the corresponding fixed boundary value problem of the hyperbolic-elliptic mixed type by building some powerful estimates for both the first-order hyperbolic equation and a second-order nonlinear elliptic equation in a Lipschitz domain; (2) we update the new free boundary by constructing a mapping that has a fixed point; (3) we establish via the inverse Lagrangian coordinate transformation that the original free interface problem admits a unique piecewise smooth transonic solution near the background state, which consists of a smooth subsonic flow and a smooth supersonic flow with a contact discontinuity.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"7 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2021-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-021-00113-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50509261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Incompressible Euler Limit from Boltzmann Equation with Diffuse Boundary Condition for Analytic Data 具有扩散边界条件的Boltzmann方程的不可压缩Euler极限

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-27 DOI: 10.1007/s40818-021-00108-z

Juhi Jang, Chanwoo Kim

{"title":"Incompressible Euler Limit from Boltzmann Equation with Diffuse Boundary Condition for Analytic Data","authors":"Juhi Jang, Chanwoo Kim","doi":"10.1007/s40818-021-00108-z","DOIUrl":"10.1007/s40818-021-00108-z","url":null,"abstract":"<div><p>A rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation with the diffuse reflection boundary condition has been a challenging open problem. We settle this open question in the affirmative when the initial data of fluid are well-prepared in a real analytic space, in 3D half space. As a key of this advance, we capture the Navier-Stokes equations of </p><div><div><span>$$begin{aligned} textit{viscosity} sim frac{textit{Knudsen number}}{textit{Mach number}} end{aligned}$$</span></div></div><p>satisfying the no-slip boundary condition, as an <i>intermediary</i> approximation of the Euler equations through a new Hilbert-type expansion of the Boltzmann equation with the diffuse reflection boundary condition. Aiming to justify the approximation we establish a novel quantitative <span>(L^p)</span>-<span>(L^infty )</span> estimate of the Boltzmann perturbation around a local Maxwellian of such viscous approximation, along with the commutator estimates and the integrability gain of the hydrodynamic part in various spaces; we also establish direct estimates of the Navier-Stokes equations in higher regularity with the aid of the initial-boundary and boundary layer weights using a recent Green’s function approach. The incompressible Euler limit follows as a byproduct of our framework.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"7 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40818-021-00108-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50517041","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}

引用次数: 20

Euler Equations on General Planar Domains 一般平面域上的欧拉方程

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-25 DOI: 10.1007/s40818-021-00107-0

Zonglin Han, Andrej Zlatoš

{"title":"Euler Equations on General Planar Domains","authors":"Zonglin Han, Andrej Zlatoš","doi":"10.1007/s40818-021-00107-0","DOIUrl":"10.1007/s40818-021-00107-0","url":null,"abstract":"<div><p>We obtain a general sufficient condition on the geometry of possibly singular planar domains that guarantees global uniqueness for any weak solution to the Euler equations on them whose vorticity is bounded and initially constant near the boundary. While similar existing results require domains that are <span>(C^{1,1})</span> except at finitely many convex corners, our condition involves much less domain smoothness, being only slightly more restrictive than the exclusion of corners with angles greater than <span>(pi )</span>. In particular, it is satisfied by all convex domains. The main ingredient in our approach is showing that constancy of the vorticity near the boundary is preserved for all time because Euler particle trajectories on these domains, even for general bounded solutions, cannot reach the boundary in finite time. We then use this to show that no vorticity can be created by the boundary of such possibly singular domains for general bounded solutions. We also show that our condition is essentially sharp in this sense by constructing domains that come arbitrarily close to satisfying it, and on which particle trajectories can reach the boundary in finite time. In addition, when the condition is satisfied, we find sharp bounds on the asymptotic rate of the fastest possible approach of particle trajectories to the boundary.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"7 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40818-021-00107-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50511555","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}

引用次数: 6

Global Well-Posedness for the Fifth-Order KdV Equation in (H^{-1}(pmb {mathbb {R}})) 五阶KdV方程在（H^｛-1｝（pmb｛mathbb｛R｝）中的全局适定性

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-25 DOI: 10.1007/s40818-021-00111-4

Bjoern Bringmann, Rowan Killip, Monica Visan

引用次数: 7

Maximal (L^q)-Regularity for Parabolic Hamilton–Jacobi Equations and Applications to Mean Field Games 抛物型Hamilton–Jacobi方程的极大正则性及其在平均场对策中的应用

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-22 DOI: 10.1007/s40818-021-00109-y

Marco Cirant, Alessandro Goffi

引用次数: 20

Asymptotic Stability of Equilibria for Screened Vlasov–Poisson Systems via Pointwise Dispersive Estimates 基于点分散估计的屏蔽Vlasov–Poisson系统平衡的渐近稳定性

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-20 DOI: 10.1007/s40818-021-00110-5

Daniel Han-Kwan, Toan T. Nguyen, Frédéric Rousset

引用次数: 25

Variational Approach to Regularity of Optimal Transport Maps: General Cost Functions 最优运输图正则性的变分方法：一般成本函数

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-18 DOI: 10.1007/s40818-021-00106-1

Felix Otto, Maxime Prod’homme, Tobias Ried

引用次数: 7

Coordinates at Small Energy and Refined Profiles for the Nonlinear Schrödinger Equation 非线性Schrödinger方程的小能量坐标和精细轮廓

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-07-20 DOI: 10.1007/s40818-021-00105-2

Scipio Cuccagna, Masaya Maeda

引用次数: 12

Stability of Solitary Waves for the Modified Camassa-Holm Equation 修正Camassa-Holm方程孤立波的稳定性

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-06-05 DOI: 10.1007/s40818-021-00104-3

Ji Li, Yue Liu

引用次数: 5

Stability of Vacuum for the Boltzmann Equation with Moderately Soft Potentials 中等软势Boltzmann方程的真空稳定性

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-06-05 DOI: 10.1007/s40818-021-00103-4

Sanchit Chaturvedi

{"title":"Stability of Vacuum for the Boltzmann Equation with Moderately Soft Potentials","authors":"Sanchit Chaturvedi","doi":"10.1007/s40818-021-00103-4","DOIUrl":"10.1007/s40818-021-00103-4","url":null,"abstract":"<div><p>We consider the spatially inhomogeneous non-cutoff Boltzmann equation with moderately soft potentials and any singularity parameter <span>(sin (0,1))</span>, i.e. with <span>(gamma +2sin (0,2))</span> on the whole space <span>({mathbb {R}}^3)</span>. We prove that if the initial data <span>(f_{{{,mathrm{in},}}})</span> are close to the vacuum solution <span>(f_{text {vac}}=0)</span> in an appropriate weighted norm then the solution <i>f</i> remains regular globally in time and approaches a solution to a linear transport equation. Our proof uses <span>(L^2)</span> estimates and we prove a multitude of new estimates involving the Boltzmann kernel without angular cut-off. Moreover, we rely on various previous works including those of Gressman–Strain, Henderson–Snelson–Tarfulea and Silvestre. From the point of view of the long time behavior we treat the Boltzmann collisional operator perturbatively. Thus an important challenge of this problem is to exploit the dispersive properties of the transport operator to prove integrable time decay of the collisional operator. This requires the most care and to successfully overcome this difficulty we draw inspiration from Luk’s work [Stability of vacuum for the Landau equation with moderately soft potentials, Annals of PDE (2019) 5:11] and that of Smulevici [Small data solutions of the Vlasov-Poisson system and the vector field method, Ann. PDE, 2(2):Art. 11, 55, 2016]. In particular, to get at least integrable time decay we need to consolidate the decay coming from the space-time weights and the decay coming from commuting vector fields.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"7 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40818-021-00103-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50452877","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}

引用次数: 9