Related papers: The noncommutative MMP for blowup surfaces
We define a geometric flow that is designed to change surfaces of cylindrical type spanning two disjoint boundary curves into solutions of the Douglas-Plateau problem of finding minimal surfaces with given boundary curves. We prove that…
We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link…
One of the major open problems in noncommutative algebraic geometry is the classification of noncommutative projective surfaces (or, slightly more generally, of noetherian connected graded domains of Gelfand-Kirillov dimension 3). In a…
The aim of this paper is to consider quasi-linear systems which are not in the form of evolution equations. We propose new condition of Richness or Semi-Hamiltonicity for such a system and prove that the blow up analysis along…
This paper is devoted to the analysis of blow-up solutions for the fractional nonlinear Schr\"odinger equation with combined power-type nonlinearities \[ i\partial_t u-(-\Delta)^su+\lambda_1|u|^{2p_1}u+\lambda_2|u|^{2p_2}u=0, \] where…
In this paper, we study the interaction between a nonlinear focusing Robin type boundary source, a nonlinear defocusing interior source, and a weak damping term for nonlinear Schr\"odinger equations posed on the infinite half line. We…
An improvement of [18] on the blow-up region and the lifespan estimate of a weakly coupled system of wave equations with damping and mass in the scale-invariant case and with time-derivative nonlinearity is obtained in this article. Indeed,…
We construct a quasiconformally homogeneous hyperbolic Riemann surface-other than the hyperbolic plane-that does not admit a bounded pants decomposition. Also, given a connected orientable topological surface of infinite type with compact…
We give a sufficient condition for blow up of positive mild solutions to an initial value problem for a nonautonomous weakly coupled system with distinct fractional diffusions. The proof is based on the study of blow up of a particular…
We develop a reduction scheme \`a la Marsden-Weinstein-Meyer for hybrid Hamiltonian systems. Our method does not require the momentum map to be equivariant, neither to be preserved by the impact map. We illustrate the applicability of our…
We study the focusing mass-critical rough nonlinear Schroedinger equations, where the stochastic integration is taken in the sense of controlled rough path. We obtain the global well-posedness if the mass of initial data is below that of…
The purpose of this paper is to investigate the Cahn-Hillard approximation for entire minimal hypersurfaces in the hyperbolic space. Combining comparison principles with minimization and blow-up arguments, we prove existence results for…
We decrease the $rms$ mean curvature and area of a variable surface with a fixed boundary by iterating a few times through a curvature-based variational algorithm. For a boundary with a known minimal surface, starting with a deliberately…
We study the well-posedness of a modified degenerate Cahn-Hilliard type model for surface diffusion. With degenerate phase-dependent diffusion mobility and additional stabilizing function, this model is able to give the correct sharp…
Thin-walled structures clamped by friction joints, such as aircraft skin panels are exposed to bending-stretching coupling and frictional contact. We propose an original sub-structuring approach, where the system is divided into thin-walled…
The stabilization of long-range magnetic order in nominally non-magnetic semi-conductors using femtosecond light pulses is an exciting yet experimentally challenging goal. Theoretical studies indicate that certain non-magnetic…
The aim of this paper is to collect some facts about the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in…
We consider a semiclassical linear Boltzmann model with a non local collision operator. We provide sharp spectral asymptotics for the small spectrum in the low temperature regime from which we deduce the rate of return to equilibrium as…
For the Schr\"odinger map problem from 2+1 dimensions into the 2-sphere we prove the existence of equivariant finite time blow up solutions that are close to a dynamically rescaled lowest energy harmonic map, the scaling parameter being…
This paper deals with the quasilinear parabolic-elliptic chemotaxis system with logistic source and nonlinear production, \begin{equation*} \begin{cases} u_t=\nabla \cdot (D(u) \nabla u) - \nabla \cdot (S(u)\nabla v) + \lambda u - \mu…