Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8867
Changzhen Song, Xinying Xu, Jianwen Zhang
Abstract. In this paper, we consider the Cauchy problem of the full Navier-Stokes equations for three-dimensional compressible viscous heat-conducting flows subject to external potential forces in the whole space R3 . For discontinuous data with small energy and vacuum, the global “intermediate weak” solutions with large oscillations and large external potential forces are obtained, provided the unique steady state is strictly away from vacuum. Moreover, if ‖∇ρ0‖L2∩Lp with any p ∈ (3, 6), ‖∇u0‖L3 and ‖∇θ0‖L2 are bounded, then the weak solution becomes a strong one belonging to a class of functions in which the uniqueness can be shown to hold, when the density is strictly away from vacuum and the viscosity coefficients satisfy 7μ > λ additionally.
{"title":"On the Cauchy problem of the full Navier-Stokes equations for three-dimensional compressible viscous heat-conducting flows subject to large external potential forces","authors":"Changzhen Song, Xinying Xu, Jianwen Zhang","doi":"10.1512/iumj.2022.71.8867","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8867","url":null,"abstract":"Abstract. In this paper, we consider the Cauchy problem of the full Navier-Stokes equations for three-dimensional compressible viscous heat-conducting flows subject to external potential forces in the whole space R3 . For discontinuous data with small energy and vacuum, the global “intermediate weak” solutions with large oscillations and large external potential forces are obtained, provided the unique steady state is strictly away from vacuum. Moreover, if ‖∇ρ0‖L2∩Lp with any p ∈ (3, 6), ‖∇u0‖L3 and ‖∇θ0‖L2 are bounded, then the weak solution becomes a strong one belonging to a class of functions in which the uniqueness can be shown to hold, when the density is strictly away from vacuum and the viscosity coefficients satisfy 7μ > λ additionally.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765078","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}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8873
Li-Xiang An, Xin-Han Dong, Xinggang He
{"title":"On spectra and spectral eigenmatrix problems of the planar Sierpinski measures","authors":"Li-Xiang An, Xin-Han Dong, Xinggang He","doi":"10.1512/iumj.2022.71.8873","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8873","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765476","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}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.9188
D. Karmakar, G. Wolansky
{"title":"On the critical mass Patlak-Keller-Segel system for multi-species populations: global existence and infinte time aggregation","authors":"D. Karmakar, G. Wolansky","doi":"10.1512/iumj.2022.71.9188","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.9188","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765849","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}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8789
Z. Bradshaw, I. Kukavica, Tai-Peng Tsai
{"title":"Existence of global weak solutions to the Navier-Stokes equations in weighted spaces","authors":"Z. Bradshaw, I. Kukavica, Tai-Peng Tsai","doi":"10.1512/iumj.2022.71.8789","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8789","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66764853","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}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.9075
G. Galdi
{"title":"Existence, uniqueness and asymptotic behavior of regular time-periodic solutions to the Navier-Stokes equations around a moving body: rotational case","authors":"G. Galdi","doi":"10.1512/iumj.2022.71.9075","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.9075","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765785","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}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8925
Lili Fan, Lizhi Ruan, Wei Xiang
This paper is devoted to the study of the initial-boundary value problem for the radiative full Euler equations, which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena. It turns out that the pattern of the asymptotic states is not unique and depends on the data both on the boundary and at the far field. In this paper, we focus our attention on the outflow problem when the flow velocity on the boundary is negative, and give a rigorous proof of the asymptotic stability of the rarefaction wave without restrictions on the smallness of the wave strength. Different from our previous work on the inflow problem for the radiative Euler equations in [6], lack of boundary conditions on the density and velocity prevents us from applying the integration by part to derive the energy estimates directly. So the outflow problem is more challenging in mathematical analysis than the inflow problem studied in [6]. New weighted energy estimates are introduced and the trace of the density and velocity on the boundary are handled by some subtle analysis. The weight is chosen based on the new observation on the key decay properties of the smooth rarefaction wave. Our investigations on the inflow and outflow problem provide a good understanding on the radiative effect and boundary effect in the setting of rarefaction wave.
{"title":"Global stability of rarefaction wave for the outflow problem governed by the radiative Euler equations","authors":"Lili Fan, Lizhi Ruan, Wei Xiang","doi":"10.1512/iumj.2022.71.8925","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8925","url":null,"abstract":"This paper is devoted to the study of the initial-boundary value problem for the radiative full Euler equations, which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena. It turns out that the pattern of the asymptotic states is not unique and depends on the data both on the boundary and at the far field. In this paper, we focus our attention on the outflow problem when the flow velocity on the boundary is negative, and give a rigorous proof of the asymptotic stability of the rarefaction wave without restrictions on the smallness of the wave strength. Different from our previous work on the inflow problem for the radiative Euler equations in [6], lack of boundary conditions on the density and velocity prevents us from applying the integration by part to derive the energy estimates directly. So the outflow problem is more challenging in mathematical analysis than the inflow problem studied in [6]. New weighted energy estimates are introduced and the trace of the density and velocity on the boundary are handled by some subtle analysis. The weight is chosen based on the new observation on the key decay properties of the smooth rarefaction wave. Our investigations on the inflow and outflow problem provide a good understanding on the radiative effect and boundary effect in the setting of rarefaction wave.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765672","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}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8850
Hiroshi Matsuzawa, H. Monobe, M. Shimojo, E. Yanagida
{"title":"Convergence to a traveling wave in the lgarithmic diffusion equation with a bistable nonlinearity","authors":"Hiroshi Matsuzawa, H. Monobe, M. Shimojo, E. Yanagida","doi":"10.1512/iumj.2022.71.8850","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8850","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765022","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}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8921
Oscar Rivero Salgado
{"title":"Generalized Kato classes and exceptional zero conjectures","authors":"Oscar Rivero Salgado","doi":"10.1512/iumj.2022.71.8921","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8921","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765331","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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