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Which Measure-Valued Solutions of the Monoatomic Gas Equations are Generated by Weak Solutions?
Contrary to the incompressible case, not every measure-valued solution of the compressible Euler equations can be generated by weak solutions or a...
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Weak Solutions of 3D Compressible Navier–Stokes Equations in Critical Case
New estimates of the potentials of solutions to the compressible Navier–Stokes equations are derived. The result obtained are applied to boundary...
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A Priori Estimates for Solutions to Landau Equation Under Prodi–Serrin Like Criteria
In this paper, we introduce Prodi–Serrin like criteria which enable us to provide a priori estimates for the solutions to the spatially homogeneous...
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A Numerical Approach for the Existence of Dissipative Weak Solutions to a Compressible Two-fluid Model
As an extension of the recent work of Novotný et al. (J Elliptic Parabol Equ 7:537–570 2021), we study the dissipative weak solutions to a...
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Well-Posedness of Solutions to Stochastic Fluid–Structure Interaction
In this paper we introduce a constructive approach to study well-posedness of solutions to stochastic fluid–structure interaction with stochastic...
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Global Existence of Strong and Weak Solutions to 2D Compressible Navier–Stokes System in Bounded Domains with Large Data and Vacuum
The barotropic compressible Navier–Stokes system subject to the Navier-slip boundary conditions in a general two-dimensional bounded simply connected...
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Non-uniqueness of Steady-State Weak Solutions to the Surface Quasi-Geostrophic Equations
We show the existence of nontrivial stationary weak solutions to the surface quasi-geostrophic equations on the two dimensional periodic torus.
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Compressible Fluids Interacting with Plates: Regularity and Weak-Strong Uniqueness
In this paper, we study a nonlinear interaction problem between compressible viscous fluids and plates. For this problem, we introduce relative...
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Global Finite-Energy Solutions of the Compressible Euler–Poisson Equations for General Pressure Laws with Large Initial Data of Spherical Symmetry
We are concerned with global finite-energy solutions of the three-dimensional compressible Euler–Poisson equations with gravitational potential and gen...
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On Weak-Strong Uniqueness for Stochastic Equations of Incompressible Fluid Flow
We introduce a concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing the motion of an inviscid...
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Global Regular Axially-Symmetric Solutions to the Navier–Stokes Equations with Small Swirl
Axially symmetric solutions to the Navier–Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity...
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Local Existence of Solutions to a Navier–Stokes-Nonlinear-Schrödinger Model of Superfluidity
In Pitaevskii (Sov Phys JETP 35(8):282–287, 1959), a micro-scale model of superfluidity was derived from first principles, to describe the...
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Dissipative Solutions to Compressible Navier–Stokes Equations with General Inflow–Outflow Data: Existence, Stability and Weak Strong Uniqueness
So far existence of dissipative weak solutions for the compressible Navier–Stokes equations (i.e. weak solutions satisfying the relative energy...
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The Long-Wave Approximation for the Green–Naghdi System with the Weak Coriolis Effect
The issue studied in the present paper is the long-wave approximation to the rotation-Green–Naghdi system, which is considered as a model for the...
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