In this paper we prove the local well-posedness of strong solutions to a chemotaxisshallow water system with initial vacuum in a bounded domainΩ■R^(2)without the standard compatibility condition for the initial data...In this paper we prove the local well-posedness of strong solutions to a chemotaxisshallow water system with initial vacuum in a bounded domainΩ■R^(2)without the standard compatibility condition for the initial data.This improves some results obtained in[J.Differential Equations 261(2016),6758-6789].展开更多
We consider base spaces of Lagrangian fibrations from singular symplectic varieties. After defining cohomologically irreducible symplectic varieties, we construct an example of Lagrar, gian fibration whose base space ...We consider base spaces of Lagrangian fibrations from singular symplectic varieties. After defining cohomologically irreducible symplectic varieties, we construct an example of Lagrar, gian fibration whose base space is isomorphic to a quotient of the projective space. We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth.展开更多
This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ i...This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ in the energy norm, and to show it has a free profile as t →+∞. Our approach is based on the work of [11]. Namely we use a weighted L^∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.展开更多
Demoulin surfaces in the real projective 3-space are investigated. Our result enables us to establish a generalized Weierstrass type representation for definite Demoulin surfaces by virtue of primitive maps into a cer...Demoulin surfaces in the real projective 3-space are investigated. Our result enables us to establish a generalized Weierstrass type representation for definite Demoulin surfaces by virtue of primitive maps into a certain semi-Riemannian 6-symmetric space.展开更多
To quantify fluorescence imaging of biological tissues,we need to solve an inverse problem for the coupled radiative transfer equations which describe the excitation and emission fields in biological tissues.We begin ...To quantify fluorescence imaging of biological tissues,we need to solve an inverse problem for the coupled radiative transfer equations which describe the excitation and emission fields in biological tissues.We begin by giving a concise mathematical argument to derive coupled diffusion equations with the Robin boundary condition as an approximation of the radiative transfer system.Then by using this coupled system of equations as a model for the fluorescence imaging,we have a nonlinear inverse problem to identify the absorption coefficient in this system.The associated linearized inverse problem is to ignore the absorbing effect on the excitation field.We firstly establish the estimates of errors on the excitation field and the solution to the inverse problem,which ensures the reasonability of the model approximation quantitatively.Some numerical verification is presented to show the validity of such a linearizing process quantitatively.Then,based on the analytic expressions of excitation and emission fields,the identifiability of the absorption coefficient from the linearized inverse problem is rigorously analyzed for the absorption coefficient in the special form,revealing the physical difficulty of the3-dimensional imaging model by the back scattering diffusive system.展开更多
In this paper, we present the theory and numerical implementation for a 2-D thermal inhomogeneity through the dynamical probe method. The main idea of the dynamical probe method is to construct an indicator function a...In this paper, we present the theory and numerical implementation for a 2-D thermal inhomogeneity through the dynamical probe method. The main idea of the dynamical probe method is to construct an indicator function associated with some probe such that when the probe touch the boundary of the inclusion the indicator function will blow up. From this property, we can get the shape of the inclusion. We will give the numerical reconstruction algorithm to identify the inclusion from the simulated Neumann-to-Dirichlet map.展开更多
In this paper we prove the local well-posedness of strong solutions to the compressible nematic liquid crystals flow with vacuum in a bounded domainΩ■R3.
In this paper we first establish the uniform regularity of smooth solutions with respect to the viscosity coefficients to the isentropic compressible magnetohydrodynamic system in a periodic domain T;.We then apply ou...In this paper we first establish the uniform regularity of smooth solutions with respect to the viscosity coefficients to the isentropic compressible magnetohydrodynamic system in a periodic domain T;.We then apply our result to obtain the isentropic compressible magnetohydrodynamic system with zero viscosity.展开更多
We prove two new regularity criteria for the 3D incompressible Navier-Stokes equations in a bounded domain. Our results also hold for the 3D Boussinesq system with zero heat conductivity.
基金supported by NSFC(11971234)supported in part by NSFC(11671193)A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In this paper we prove the local well-posedness of strong solutions to a chemotaxisshallow water system with initial vacuum in a bounded domainΩ■R^(2)without the standard compatibility condition for the initial data.This improves some results obtained in[J.Differential Equations 261(2016),6758-6789].
基金supported by Japan Society for Promotion of Sciences(Grant No.18684001)
文摘We consider base spaces of Lagrangian fibrations from singular symplectic varieties. After defining cohomologically irreducible symplectic varieties, we construct an example of Lagrar, gian fibration whose base space is isomorphic to a quotient of the projective space. We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth.
基金Project supported by Grant-in-Aid for Science Research (No.12740105, No.14204011), JSPS.
文摘This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ in the energy norm, and to show it has a free profile as t →+∞. Our approach is based on the work of [11]. Namely we use a weighted L^∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.
基金supported by JSPS KAKENHI (Grant Nos. JP18K03265 and JP19K03461)。
文摘Demoulin surfaces in the real projective 3-space are investigated. Our result enables us to establish a generalized Weierstrass type representation for definite Demoulin surfaces by virtue of primitive maps into a certain semi-Riemannian 6-symmetric space.
基金supported by National Natural Science Foundation of China(Grant Nos.11531005,11971104 and 11421110002)supported by Grant-in-Aid for Scientific Research of the Japan Society for the Promotion of Science(JSPS)(Grant Nos.17K05572 and 17H02081)+2 种基金from the JSPS A3 foresight program:Modeling and Computation of Applied Inverse Problemssupported by Grant-in-Aid for Scientific Research of the JSPS(Grant Nos.19K03554 and 15H05740)supported by Grant-in-Aid for Scientific Research of the JSPS(Grant No.19K04421)。
文摘To quantify fluorescence imaging of biological tissues,we need to solve an inverse problem for the coupled radiative transfer equations which describe the excitation and emission fields in biological tissues.We begin by giving a concise mathematical argument to derive coupled diffusion equations with the Robin boundary condition as an approximation of the radiative transfer system.Then by using this coupled system of equations as a model for the fluorescence imaging,we have a nonlinear inverse problem to identify the absorption coefficient in this system.The associated linearized inverse problem is to ignore the absorbing effect on the excitation field.We firstly establish the estimates of errors on the excitation field and the solution to the inverse problem,which ensures the reasonability of the model approximation quantitatively.Some numerical verification is presented to show the validity of such a linearizing process quantitatively.Then,based on the analytic expressions of excitation and emission fields,the identifiability of the absorption coefficient from the linearized inverse problem is rigorously analyzed for the absorption coefficient in the special form,revealing the physical difficulty of the3-dimensional imaging model by the back scattering diffusive system.
基金supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) under the grant number KRF-2006-214-C00007
文摘In this paper, we present the theory and numerical implementation for a 2-D thermal inhomogeneity through the dynamical probe method. The main idea of the dynamical probe method is to construct an indicator function associated with some probe such that when the probe touch the boundary of the inclusion the indicator function will blow up. From this property, we can get the shape of the inclusion. We will give the numerical reconstruction algorithm to identify the inclusion from the simulated Neumann-to-Dirichlet map.
基金Fan is supported by NSFC(Grant No.11971234).Li is supported by NSFC(Grant No.11671193)and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘In this paper we prove the local well-posedness of strong solutions to the compressible nematic liquid crystals flow with vacuum in a bounded domainΩ■R3.
基金Tsupported by the National Natural Science Foundation of China(No.11971234,11671193)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In this paper we first establish the uniform regularity of smooth solutions with respect to the viscosity coefficients to the isentropic compressible magnetohydrodynamic system in a periodic domain T;.We then apply our result to obtain the isentropic compressible magnetohydrodynamic system with zero viscosity.
基金Acknowledgements Fan was supported by the National Natural Science Foundation of China (Grant No. 11171154) Li was supported by the National Natural Science Foundation of China (Grant Nos. 11271184, 11671193) and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘We prove two new regularity criteria for the 3D incompressible Navier-Stokes equations in a bounded domain. Our results also hold for the 3D Boussinesq system with zero heat conductivity.