Journal of Mathematical Fluid Mechanics最新文献

{"title":"Global Existence of Strong Solutions and Serrin-Type Blowup Criterion for 3D Combustion Model in Bounded Domains","authors":"Jiawen Zhang","doi":"10.1007/s00021-023-00830-7","DOIUrl":"10.1007/s00021-023-00830-7","url":null,"abstract":"<div><p>The combustion model is studied in three-dimensional (3D) smooth bounded domains with various types of boundary conditions. The global existence and uniqueness of strong solutions are obtained under the smallness of the gradient of initial velocity in some precise sense. Using the energy method with the estimates of boundary integrals, we obtain the a priori bounds of the density and velocity field. Finally, we establish the blowup criterion for the 3D combustion system.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Stability and Decay for the 2D Incompressible Euler-Like Equations","authors":"Hongxia Lin,&nbsp;Qing Sun,&nbsp;Sen Liu,&nbsp;Heng Zhang","doi":"10.1007/s00021-023-00824-5","DOIUrl":"10.1007/s00021-023-00824-5","url":null,"abstract":"<div><p>This paper is concerned with the two-dimensional incompressible Euler-like equations. More precisely, we consider the system with only damping in the vertical component equation. When the domain is the whole space <span>(mathbb {R}^2)</span>, it is well known that solutions of the incompressible Euler equations can grow rapidly in time while solutions of the Euler equations with full damping are stable. As the intermediate case of the two equations, the global well-posedness and the stability in <span>(mathbb {R}^2)</span> remain the outstanding open problem. Our attentions here focus on the domain <span>(Omega =mathbb {T}times mathbb {R})</span> with <span>(mathbb {T})</span> being 1D periodic box. Compared with <span>(mathbb {R}^2)</span>, the domain <span>(Omega )</span> allows us to separate the physical quantity <i>f</i> into its horizontal average <span>(overline{f})</span> and the corresponding oscillation <span>(widetilde{f})</span>. By deriving the strong Poincaré inequality and two anisotropic inequalities related to <span>(widetilde{f})</span>, we are able to employ the time-weighted energy estimate to establish the stability of the solution and the precise large-time behavior of the system provided that the initial data is small and satisfies the reflection symmetry condition.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical Theory of Compressible Magnetohydrodynamics Driven by Non-conservative Boundary Conditions","authors":"Eduard Feireisl,&nbsp;Piotr Gwiazda,&nbsp;Young-Sam Kwon,&nbsp;Agnieszka Świerczewska-Gwiazda","doi":"10.1007/s00021-023-00827-2","DOIUrl":"10.1007/s00021-023-00827-2","url":null,"abstract":"<div><p>We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by ihomogeneous boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime characteristic for turbulence. The weak solutions comply with the weak–strong uniqueness principle; they coincide with the classical solution of the problem as long as the latter exists. The choice of constitutive relations is motivated by applications in stellar magnetoconvection.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00827-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fast Rotating Non-homogeneous Fluids in Thin Domains and the Ekman Pumping Effect","authors":"Marco Bravin,&nbsp;Francesco Fanelli","doi":"10.1007/s00021-023-00826-3","DOIUrl":"10.1007/s00021-023-00826-3","url":null,"abstract":"<div><p>In this paper, we perform the fast rotation limit <span>(varepsilon rightarrow 0^+)</span> of the density-dependent incompressible Navier–Stokes–Coriolis system in a thin strip <span>(Omega _varepsilon :=,{mathbb {R}}^2times , left. right] -ell _varepsilon ,ell _varepsilon left[ right. ,)</span>, where <span>(varepsilon in ,left. right] 0,1left. right] )</span> is the size of the Rossby number and <span>(ell _varepsilon &gt;0)</span> for any <span>(varepsilon &gt;0)</span>. By letting <span>(ell _varepsilon longrightarrow 0^+)</span> for <span>(varepsilon rightarrow 0^+)</span> and considering Navier-slip boundary conditions at the boundary of <span>(Omega _varepsilon )</span>, we give a rigorous justification of the phenomenon of the Ekman pumping in the context of non-homogeneous fluids. With respect to previous studies (performed for flows of contant density and for compressible fluids), our approach has the advantage of circumventing the complicated analysis of boundary layers. To the best of our knowledge, this is the first study dealing with the asymptotic analysis of fast rotating incompressible fluids with variable density in a 3-D setting. In this respect, we remark that the case <span>(ell _varepsilon geqslant ell &gt;0)</span> for all <span>(varepsilon &gt;0)</span> remains largely open at present.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00826-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetrization and Local Existence of Strong Solutions for Diffuse Interface Fluid Models","authors":"Vincent Giovangigli,&nbsp;Yoann Le Calvez,&nbsp;Flore Nabet","doi":"10.1007/s00021-023-00825-4","DOIUrl":"10.1007/s00021-023-00825-4","url":null,"abstract":"<div><p>We investigate compressible nonisothermal diffuse interface fluid models also termed capillary fluids. Such fluid models involve van der Waals’ gradient energy, Korteweg’s tensor, Dunn and Serrin’s heat flux as well as diffusive fluxes. The density gradient is added as an extra variable and the convective and capillary fluxes of the augmented system are identified by using the Legendre transform of entropy. The augmented system of equations is recast into a normal form with symmetric hyperbolic first order terms, symmetric dissipative second order terms and antisymmetric capillary second order terms. New a priori estimates are obtained for such augmented system of equations in normal form. The time derivatives of the parabolic components are less regular than for standard hyperbolic–parabolic systems and the strongly coupling antisymmetric fluxes yields new majorizing terms. Using the augmented system in normal form and the a priori estimates, local existence of strong solutions is established in an Hilbertian framework.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interaction of Finitely-Strained Viscoelastic Multipolar Solids and Fluids by an Eulerian Approach","authors":"Tomáš Roubíček","doi":"10.1007/s00021-023-00817-4","DOIUrl":"10.1007/s00021-023-00817-4","url":null,"abstract":"<div><p>A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin–Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The no-slip contact between fluid and solid is considered and the Eulerian-frame return-mapping technique is used for both the fluid and the solid models, which allows for a “monolithic” formulation of this fluid–structure interaction problem. Existence and a certain regularity of weak solutions is proved by a Schauder fixed-point argument combined with a suitable regularization.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gevrey-Class-3 Regularity of the Linearised Hyperbolic Prandtl System on a Strip","authors":"Francesco De Anna,&nbsp;Joshua Kortum,&nbsp;Stefano Scrobogna","doi":"10.1007/s00021-023-00821-8","DOIUrl":"10.1007/s00021-023-00821-8","url":null,"abstract":"<div><p>In the present paper, we address a physically-meaningful extension of the linearised Prandtl equations around a shear flow. Without any structural assumption, it is well-known that the optimal regularity of Prandtl is given by the class Gevrey 2 along the horizontal direction. The goal of this paper is to overcome this barrier, by dealing with the linearisation of the so-called <i>hyperbolic Prandtl equations</i> in a strip domain. We prove that the local well-posedness around a general shear flow <span>(U_{textrm{sh}}in W^{3, infty }(0,1))</span> holds true, with solutions that are Gevrey class 3 in the horizontal direction.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00821-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41487021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"2D/3D Fully Decoupled, Unconditionally Energy Stable Rotational Velocity Projection Method for Incompressible MHD System","authors":"Ke Zhang,&nbsp;Haiyan Su,&nbsp;Demin Liu","doi":"10.1007/s00021-023-00823-6","DOIUrl":"10.1007/s00021-023-00823-6","url":null,"abstract":"<div><p>The first order linear, fully decoupled rotational velocity projection scheme for settling 2D/3D incompressible magneto-hydrodynamic system is considered in this paper. The considered governing model is a strong nonlinear system and also a double saddle points system. The proposed scheme mainly apply the first order Euler semi implicit scheme for temporal discretization, delicate implicit–explicit treatments for handling the strong nonlinear terms, and the mixed finite element method is used for spatial discretization. Then the system can be transformed into a series of linear elliptic equations such that the all variables are fully decoupled. More importantly, the existence of rotational term in the proposed algorithm makes the theoretical analysis quite difficult to carry out. Therefore, with the help of a Gauge–Uzawa form that we derive the unconditional energy stability. The results of 2D/3D numerical simulations are proved compact with the theoretical analysis.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44040031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System","authors":"Shengbin Fu,&nbsp;Weiwei Wang","doi":"10.1007/s00021-023-00820-9","DOIUrl":"10.1007/s00021-023-00820-9","url":null,"abstract":"<div><p>In this paper, we are interested in the global well-posedness of the strong solutions to the Cauchy problem on the compressible magnetohydrodynamics system with Hall effect. Moreover, we establish the convergence rates of the above solutions trending towards the constant equilibrium <span>(({bar{rho }},0,bar{textbf{B}}))</span>, provided that the initial perturbation belonging to <span>(H^3({mathbb {R}}^3) cap B_{2, infty }^{-s}({mathbb {R}}^3))</span> for <span>(s in (0,frac{3}{2}])</span> is sufficiently small.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4996997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 optimal decay rates for a generic non--conservative compressible two--fluid model","authors":"Yin Li,&nbsp;Huaqiao Wang,&nbsp;Guochun Wu,&nbsp;Yinghui Zhang","doi":"10.1007/s00021-023-00822-7","DOIUrl":"10.1007/s00021-023-00822-7","url":null,"abstract":"<div><p>We investigate global existence and optimal decay rates of a generic non-conservative compressible two–fluid model with general constant viscosities and capillary coefficients, and our main purpose is three–fold: First, for any integer <span>(ell ge 3)</span>, we show that the densities and velocities converge to their corresponding equilibrium states at the <span>(L^2)</span> rate <span>((1+t)^{-frac{3}{4}})</span>, and the <i>k</i>(<span>(in [1, ell ])</span>)–order spatial derivatives of them converge to zero at the <span>(L^2)</span> rate <span>((1+t)^{-frac{3}{4}-frac{k}{2}})</span>, which are the same as ones of the compressible Navier–Stokes–Korteweg system. This can be regarded as non-straightforward generalization from the compressible Navier–Stokes–Korteweg system to the two–fluid model. Compared to the compressible Navier–Stokes–Korteweg system, many new mathematical challenges occur since the corresponding model is non-conservative, and its nonlinear structure is very terrible, and the corresponding linear system cannot be diagonalizable. One of key observations here is that to tackle with the strongly coupling terms, we will introduce the linear combination of the fraction densities (<span>(beta ^+alpha ^+rho ^++beta ^-alpha ^-rho ^-)</span>), and explore its good regularity, which is particularly better than ones of two fraction densities (<span>(alpha ^pm rho ^pm )</span>) themselves. Second, the linear combination of the fraction densities (<span>(beta ^+alpha ^+rho ^++beta ^-alpha ^-rho ^-)</span>) converges to its corresponding equilibrium state at the <span>(L^2)</span> rate <span>((1+t)^{-frac{3}{4}})</span>, and its <i>k</i>(<span>(in [1, ell ])</span>)–order spatial derivative converges to zero at the <span>(L^2)</span> rate <span>((1+t)^{-frac{3}{4}-frac{k}{2}})</span>, but the fraction densities (<span>(alpha ^pm rho ^pm )</span>) themselves converge to their corresponding equilibrium states at the <span>(L^2)</span> rate <span>((1+t)^{-frac{1}{4}})</span>, and the <i>k</i>(<span>(in [1, ell ])</span>)–order spatial derivatives of them converge to zero at the <span>(L^2)</span> rate <span>((1+t)^{-frac{1}{4}-frac{k}{2}})</span>, which are slower than ones of their linear combination (<span>(beta ^+alpha ^+rho ^++beta ^-alpha ^-rho ^-)</span>) and the densities. We think that this phenomenon should owe to the special structure of the system. Finally, for well–chosen initial data, we also prove the lower bounds on the decay rates, which are the same as those of the upper decay rates. Therefore, these decay rates are optimal for the compressible two–fluid model.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4961206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}