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Anisotropic Regularity of the Free-Boundary Problem in Compressible Ideal Magnetohydrodynamics
We consider that 3D free-boundary compressible ideal magnetohydrodynamic (MHD) system under the Rayleigh-Taylor sign condition. This describes the...
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Higher-Order Boundary Layers and Regularity for Stokes Systems over Rough Boundaries
In this paper, we study the large-scale boundary regularity for the Stokes system in periodically oscillating John domains. Our main contribution is...
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Boundary Regularity for the Steady Generalized Newtonian Flow with Shear Thickening Viscosity
We work on the boundary regularity for weak solutions to the stationary Navier–Stokes type equations with shear dependent viscosity, which shows the...
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On the Regularity of Non-scattering Anisotropic Inhomogeneities
In this paper we examine the necessary conditions for an anisotropic inhomogeneous medium to be non-scattering at a single wave number and for a...
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Epsilon Regularity for the Navier–Stokes Equations via Weak-Strong Uniqueness
We give a new concise proof of a certain one-scale epsilon regularity criterion using weak-strong uniqueness for solutions of the Navier–Stokes...
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Regularity of the Optimal Sets for a Class of Integral Shape Functionals
We prove the first regularity theorem for the free boundary of solutions to shape optimization problems involving integral functionals, for which the...
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Global Regularity of Shear Thickening Stokes System with Dirichlet Boundary Condition on Non-smooth Domains
We study a shear thickening Stokes system in a non-smooth domain. Our purpose is to derive a Calderón–Zygmund type estimate of the gradient of a...
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A Nonlinear Elliptic PDE from Atmospheric Science: Well-Posedness and Regularity at Cloud Edge
The precipitating quasi-geostrophic equations go beyond the (dry) quasi-geostrophic equations by incorporating the effects of moisture. This means...
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Regularity Criterion for the 2D Inviscid Boussinesq Equations
The question of whether the two-dimensional inviscid Boussinesq equations can develop a finite-time singularity from general initial data is a...
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The Regularity of Very Weak Solutions to Magneto-Hydrodynamics Equations
In this paper, employing the duality technique, we prove that the very weak solution of Magneto-Hydrodynamics equations is regular in
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A Kato-Type Criterion for Vanishing Viscosity Near Onsager’s Critical Regularity
We consider a vanishing viscosity sequence of weak solutions for the three-dimensional Navier–Stokes equations of incompressible fluids in a bounded...
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Hölder Regularity up to the Boundary for Critical SQG on Bounded Domains
We consider the dissipative SQG equation in bounded domains, first introduced by Constantin and Ignatova in 2016. We show global Hölder regularity up...
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On the Regularity of Optimal Transports Between Degenerate Densities
We study the most common image and informal description of the optimal transport problem for quadratic cost, also known as the second boundary value...
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A New Type of Quaternionic Regularity
I introduce a notion of quaternionic regularity using techniques based on hypertwined analysis, a refined version of general hypercomplex theory. In...
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A Revisit of the Velocity Averaging Lemma: On the Regularity of Stationary Boltzmann Equation in a Bounded Convex Domain
In the present work, we adopt the idea of velocity averaging lemma to establish regularity for stationary linearized Boltzmann equations in a bounded...
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Lipschitz Continuous Solutions of the Vlasov–Maxwell Systems with a Conductor Boundary Condition
We consider relativistic plasma particles subjected to an external gravitation force in a 3D half space whose boundary is a perfect conductor. When...
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The Spacelike-Characteristic Cauchy Problem of General Relativity in Low Regularity
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. Given initial data on a maximal spacelike...
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Boundary Value Problems and Solutions
In the previous chapters we have used the complete integrability of the stationary axisymmetric Einstein equations in vacuum to construct and to...
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Gevrey-Class-3 Regularity of the Linearised Hyperbolic Prandtl System on a Strip
In the present paper, we address a physically-meaningful extension of the linearised Prandtl equations around a shear flow. Without any structural...