THE LOCAL WELL-POSEDNESS OF A CHEMOTAXIS-SHALLOW WATER SYSTEM WITH VACUUM

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].

LOCAL WELL-POSEDNESS IN SOBOLEV SPACES WITH NEGATIVE INDICES FOR A SEVENTH ORDER DISPERSIVE EQUATION

This paper is concerned with the Cauchy problem of a seventh order dispersive equation. We prove local well-posedness with initial data in Sobolev spaces Hs（R） for negative indices of s〉-114 .

LOCAL WELL-POSEDNESS OF STRONG SOLUTIONS FOR THE NONHOMOGENEOUS MHD EQUATIONS WITH A SLIP BOUNDARY CONDITIONS

This article is concerned with the 3 D nonhomogeneous incompressible magnetohydrodynamics equations with a slip boundary conditions in bounded domain.We obtain weighted estimates of the velocity and magnetic field,and address the issue of local existence and uniqueness of strong solutions with the weaker initial data which contains vacuum states.

WELL-POSEDNESS AND PEAKON SOLUTIONS FOR A HIGHER ORDER CAMASSA-HOLM TYPE EQUATION

In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.

Local Well-Posedness and Blow Up Criterion for the Inviscid Boussinesq System in Holder Spaces

We prove the local in time existence and a blow up criterion of solution in the Holder spaces for the inviscid Boussinesq system in RN,N ≥ 2, under the assumptions that the initial values θo,uo ∈ Cr, with 1 〈 r ≠ 2.

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u= u^k(u)~α

This paper undertakes a systematic treatment of the low regularity local well-posedness and ill-posedness theory in H3 and Hs for semilinear wave equations with polynomial nonlinearity in u and (?)u. This ill-posed result concerns the focusing type equations with nonlinearity on u and (?)tu.

Local Well-Posedness for the Compressible Nematic Liquid Crystals Flow with Vacuum

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.

Local well-posedness of a multidimensional shock wave for the steady supersonic isothermal flow

In this paper, we prove the local existence, uniqueness and stability of a supersonic shock for the supersonic isothermal incoming flow past a curved cone. Major difficulties include constructing an appropriate solution and treatincg the Neumann boundary conditions and local stability condition.

THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN

In this paper,we consider a model of compressible isentropic two-fluid magneto-hydrodynamics without resistivity in a strip domain in three dimensional space.By exploiting the two-tier energy method developed in[Anal PDE,2013,6:1429–1533],we prove the global well-posedness of the governing model around a uniform magnetic field which is non-parallel to the horizontal boundary.Moreover,we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity.Compared to the work of Tan and Wang[SIAM J Math Anal,2018,50:1432–1470],we need to overcome the difficulties caused by particles.

Local Well-posedness for Linearized Degenerate MHD Boundary Layer Equations in Analytic Setting

In this note we derive MHD boundary layer equations according to viscosity and resistivity coefficients. Especially, when these viscosity and resistivity coefficients are of different orders, it leads to degenerate MHD boundary layer equations. We prove these degenerate boundary layers are stable around a steady solution.

Navigating the pathways:TAR-DNA-binding-protein-43 aggregation,axonal transport,and local synthesis in amyotrophic lateral sclerosis pathology

Neurons are highly polarized cells with axons reaching over a meter long in adult humans.To survive and maintain their proper function,neurons depend on specific mechanisms that regulate spatiotemporal signaling and metabolic events,which need to be carried out at the right place,time,and intensity.Such mechanisms include axonal transport,local synthesis,and liquid-liquid phase separations.Alterations and malfunctions in these processes are correlated to neurodegenerative diseases such as amyotrophic lateral sclerosis(ALS).

On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest.As an alternative,the stress-driven model has been recently developed.In this paper,for higher-order shear deformation beams,the ill-posed issue(i.e.,excessive mandatory boundary conditions(BCs)cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven ones.The well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG)materials.The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions.By using the generalized differential quadrature method(GDQM),the coupling governing equations are solved numerically.The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

LiDAR-Visual SLAM with Integrated Semantic and Texture Information for Enhanced Ecological Monitoring Vehicle Localization

Ecological monitoring vehicles are equipped with a range of sensors and monitoring devices designed to gather data on ecological and environmental factors.These vehicles are crucial in various fields,including environmental science research,ecological and environmental monitoring projects,disaster response,and emergency management.A key method employed in these vehicles for achieving high-precision positioning is LiDAR(lightlaser detection and ranging)-Visual Simultaneous Localization and Mapping(SLAM).However,maintaining highprecision localization in complex scenarios,such as degraded environments or when dynamic objects are present,remains a significant challenge.To address this issue,we integrate both semantic and texture information from LiDAR and cameras to enhance the robustness and efficiency of data registration.Specifically,semantic information simplifies the modeling of scene elements,reducing the reliance on dense point clouds,which can be less efficient.Meanwhile,visual texture information complements LiDAR-Visual localization by providing additional contextual details.By incorporating semantic and texture details frompaired images and point clouds,we significantly improve the quality of data association,thereby increasing the success rate of localization.This approach not only enhances the operational capabilities of ecological monitoring vehicles in complex environments but also contributes to improving the overall efficiency and effectiveness of ecological monitoring and environmental protection efforts.

Understanding the local structure and thermophysical behavior of Mg-La liquid alloys via machine learning potential

The local structure and thermophysical behavior of Mg-La liquid alloys were in-depth understood using deep potential molecular dynamic(DPMD) simulation driven via machine learning to promote the development of Mg-La alloys. The robustness of the trained deep potential(DP) model was thoroughly evaluated through several aspects, including root-mean-square errors(RMSEs), energy and force data, and structural information comparison results;the results indicate the carefully trained DP model is reliable. The component and temperature dependence of the local structure in the Mg-La liquid alloy was analyzed. The effect of Mg content in the system on the first coordination shell of the atomic pairs is the same as that of temperature. The pre-peak demonstrated in the structure factor indicates the presence of a medium-range ordered structure in the Mg-La liquid alloy, which is particularly pronounced in the 80at% Mg system and disappears at elevated temperatures. The density, self-diffusion coefficient, and shear viscosity for the Mg-La liquid alloy were predicted via DPMD simulation, the evolution patterns with Mg content and temperature were subsequently discussed, and a database was established accordingly. Finally, the mixing enthalpy and elemental activity of the Mg-La liquid alloy at 1200 K were reliably evaluated,which provides new guidance for related studies.

Local Well-posedness of the Derivative Schrödinger Equation in Higher Dimension for Any Large Data

In this paper,the authors consider the local well-posedness for the derivative Schrödinger equation in higher dimension ut-iΔu+|u|^(2)(→γ·▽u)+u^(2)(→λ·▽-u)=0,(x,t)∈R^(n)×R,→γ,→λ∈R^(n);n≥2 It is shown that the Cauchy problem of the derivative Schrödinger equation in higher dimension is locally well-posed in H^(s)(R^(n))(s>n/2)for any large initial data.Thus this result can compare with that in one dimension except for the endpoint space H^(n/2).

WELL-POSEDNESS IN CRITICAL SPACES FOR THE FULL COMPRESSIBLE MHD EQUATIONS

In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in R^N, N≥ 2, under the assumptions that the initialdensity is bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.

Notes on well-posedness for the b-family equation

The local well-posedness for the b-family equation in the critical space is studied.Applying the Littlewood-Paley decomposition method in the critical Besov spaces Bs2r with the index s=3/2 which is the generalization space of the Sobolev spaces Hs it is established that there is a maximal time T=Tu0＆gt;0 such that for the b-family equation there exists a unique solution utx∈C0TB3/221∩C10TB121 when the initial variable u0x ∈B3/221 is the critical regularity. Moreover the solution uxt depends continuously on the initial data u0x .Furthermore using the abstract Cauchy-Kowalevski theorem to prove the analytic regularity of the solutions for the b-family equation in a suitable scale of Banach spaces E it is shown that the solutions of the b-family are analytic in both variables globally in space and locally in time when the initial data is analytic.

GLOBAL WELL-POSEDNESS OF THE STOCHASTIC 2D BOUSSINESQ EQUATIONS WITH PARTIAL VISCOSITY

This paper deals with the stochastic 2D Boussinesq equations with partial viscosity. This is a coupled system of Navier-Stokes/Euler equations and the transport equation for temperature under additive noise. Global well-posedness result of this system under partial viscosity is proved by using classical energy estimates method.

GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F N^(s(·))p(·),h(·),q(R^(3))with s(·)=4-2α-3/p(·).We prove global well-posedness result with small initial data belonging to FN^(4-2α-3/p(·))p(·),h(·)q(R^(3)).The result of this paper extends some recent work.

THE WELL-POSEDNESS AND ASYMPTOTICS OF MULTI-DIMENSIONAL QUANTUM HYDRODYNAMICS

The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up in quantum wells） take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.